Trust in Artificial Intelligent Agents Scale

First quantitative approbation. Data analysis workflow

Preprocess

Find preprocess workflow here.

Packages

library(tidyverse)
library(psych)
library(lavaan)
library(semPlot)
library(knitr)
library(corrplot)

theme_set(theme_bw())

Import data

taia <- read_csv("https://github.com/angelgardt/taia/raw/master/data/taia.csv")
str(taia)

tibble [495 × 133] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
 $ id         : chr [1:495] "00XzIUUVmQ" "0aABrq9MBY" "0c6myGTrKr" "0CS5iaAVos" ...
 $ e_dighelp  : num [1:495] 5 NA 4 3.33 3 ...
 $ n_dighelp  : num [1:495] 1 NA 1 3 2 1 3 2 4 1 ...
 $ e_socnet   : num [1:495] 0 NA 3.2 3.6 4.5 ...
 $ f_socnet   : num [1:495] 3 NA 2.4 1.6 2 ...
 $ n_socnet   : num [1:495] 2 NA 5 5 2 2 2 4 3 4 ...
 $ gt_score   : num [1:495] 2.67 2.67 2.83 2.5 2.67 ...
 $ pr01       : num [1:495] 3 3 3 3 3 4 3 1 3 4 ...
 $ pr02       : num [1:495] 3 3 3 3 3 3 3 1 3 3 ...
 $ pr03       : num [1:495] 3 3 3 3 3 1 5 1 3 4 ...
 $ pr04       : num [1:495] 2 3 3 3 2 0 3 2 4 3 ...
 $ pr05       : num [1:495] 3 2 1 2 3 4 4 1 0 3 ...
 $ pr06       : num [1:495] 2 2 4 3 3 5 4 3 4 4 ...
 $ pr07       : num [1:495] 3 3 3 3 3 5 3 2 1 3 ...
 $ pr08       : num [1:495] 2 3 4 2 3 4 4 4 3 4 ...
 $ pr09       : num [1:495] 2 4 3 3 4 4 4 3 3 4 ...
 $ pr10       : num [1:495] 2 3 3 2 3 4 3 3 1 3 ...
 $ co01       : num [1:495] 2 3 3 2 3 4 3 2 4 3 ...
 $ co02       : num [1:495] 3 3 3 2 3 3 3 1 2 3 ...
 $ co03       : num [1:495] 3 4 4 2 3 4 4 2 2 3 ...
 $ co04       : num [1:495] 4 2 4 4 3 5 4 3 5 4 ...
 $ co05       : num [1:495] 2 2 3 2 3 4 4 2 3 2 ...
 $ co06       : num [1:495] 3 3 4 4 3 3 4 2 2 3 ...
 $ co07       : num [1:495] 2 3 1 1 1 1 1 3 0 1 ...
 $ co08       : num [1:495] 2 2 2 1 4 5 2 1 2 1 ...
 $ co09       : num [1:495] 2 3 2 1 4 4 3 2 1 2 ...
 $ co10       : num [1:495] 3 2 3 2 3 5 3 1 1 2 ...
 $ ut01       : num [1:495] 3 4 4 5 4 5 5 4 4 3 ...
 $ ut02       : num [1:495] 2 3 3 4 4 5 5 3 3 3 ...
 $ ut03       : num [1:495] 3 2 4 5 1 5 3 4 3 3 ...
 $ ut04       : num [1:495] 3 3 3 4 4 5 4 3 2 3 ...
 $ ut05       : num [1:495] 3 2 3 5 4 3 4 3 4 3 ...
 $ ut06       : num [1:495] 2 3 4 4 4 5 4 3 3 3 ...
 $ ut07       : num [1:495] 3 2 4 5 4 4 4 3 4 3 ...
 $ ut08       : num [1:495] 3 3 3 4 4 5 4 3 4 4 ...
 $ ut09       : num [1:495] 2 3 3 3 3 4 4 3 3 4 ...
 $ ut10       : num [1:495] 2 2 2 4 1 2 2 1 3 3 ...
 $ ut11       : num [1:495] 2 2 3 4 3 2 4 1 1 3 ...
 $ ut12       : num [1:495] 3 4 4 3 4 2 4 3 3 4 ...
 $ fa01       : num [1:495] 2 2 3 4 2 2 3 3 2 2 ...
 $ fa02       : num [1:495] 2 3 2 4 2 0 2 3 2 1 ...
 $ fa03       : num [1:495] 3 3 3 1 4 2 1 0 3 2 ...
 $ fa04       : num [1:495] 2 3 3 2 1 2 2 0 1 2 ...
 $ fa05       : num [1:495] 3 3 3 3 4 4 3 3 2 3 ...
 $ fa06       : num [1:495] 3 2 4 3 3 2 4 0 2 3 ...
 $ fa07       : num [1:495] 3 3 3 3 1 3 2 1 1 3 ...
 $ fa08       : num [1:495] 3 2 2 2 1 2 2 3 2 2 ...
 $ fa09       : num [1:495] 3 2 3 4 2 1 2 3 2 2 ...
 $ fa10       : num [1:495] 2 2 2 4 1 3 3 4 4 2 ...
 $ de01       : num [1:495] 3 2 3 3 3 3 4 3 3 3 ...
 $ de02       : num [1:495] 3 3 3 3 3 4 4 2 1 3 ...
 $ de03       : num [1:495] 3 3 4 3 3 5 3 2 1 3 ...
 $ de04       : num [1:495] 2 3 2 0 2 2 0 3 1 3 ...
 $ de05       : num [1:495] 3 3 4 3 3 5 5 4 4 4 ...
 $ de06       : num [1:495] 2 3 3 3 3 3 4 0 0 3 ...
 $ de07       : num [1:495] 3 2 3 3 3 3 4 3 3 3 ...
 $ de08       : num [1:495] 3 3 3 3 3 5 4 1 1 3 ...
 $ de09       : num [1:495] 4 2 3 3 3 5 5 4 1 4 ...
 $ de10       : num [1:495] 3 3 4 3 3 3 4 3 3 3 ...
 $ de11       : num [1:495] 2 3 2 3 2 1 4 4 1 1 ...
 $ un01       : num [1:495] 3 3 3 2 4 3 4 3 4 4 ...
 $ un02       : num [1:495] 2 2 3 2 4 3 4 2 3 3 ...
 $ un03       : num [1:495] 3 1 3 3 4 5 4 2 4 3 ...
 $ un04       : num [1:495] 3 1 3 3 4 3 3 2 4 3 ...
 $ un05       : num [1:495] 3 3 4 3 4 4 4 3 4 4 ...
 $ un06       : num [1:495] 3 3 2 1 1 1 4 1 4 4 ...
 $ un07       : num [1:495] 2 3 2 2 4 4 3 1 2 3 ...
 $ un08       : num [1:495] 2 3 3 3 4 4 4 4 4 3 ...
 $ un09       : num [1:495] 2 1 4 2 4 4 4 1 2 4 ...
 $ un10       : num [1:495] 3 3 3 2 4 3 4 2 2 4 ...
 $ un11       : num [1:495] 3 2 3 2 4 4 3 3 4 3 ...
 $ un12       : num [1:495] 3 2 3 3 4 4 4 3 4 3 ...
 $ gt01       : num [1:495] 3 3 3 2 3 2 1 1 1 2 ...
 $ gt02       : num [1:495] 3 2 3 3 3 3 1 1 1 2 ...
 $ gt03       : num [1:495] 3 3 3 3 3 2 1 1 1 3 ...
 $ gt04       : num [1:495] 3 2 3 2 3 4 1 1 2 2 ...
 $ gt05       : num [1:495] 2 3 2 2 1 4 0 2 0 2 ...
 $ gt06       : num [1:495] 2 3 3 3 3 3 3 1 1 3 ...
 $ socnet     : num [1:495] 1 0 1 1 1 1 1 1 1 1 ...
 $ vk         : num [1:495] 1 -2 1 1 1 1 1 1 1 1 ...
 $ fb         : num [1:495] 0 -2 1 1 1 0 0 1 0 1 ...
 $ tw         : num [1:495] 0 -2 1 0 0 0 0 0 0 0 ...
 $ in         : num [1:495] 1 -2 1 1 0 1 1 1 1 1 ...
 $ tt         : num [1:495] 0 -2 0 1 0 0 0 0 0 0 ...
 $ yt         : num [1:495] 0 -2 1 1 0 0 0 1 1 1 ...
 $ freqvk     : num [1:495] 3 -2 3 2 3 3 3 3 3 3 ...
 $ freqfb     : num [1:495] -2 -2 2 2 1 -2 -2 0 -2 3 ...
 $ freqtw     : num [1:495] -2 -2 2 -2 -2 -2 -2 -2 -2 -2 ...
 $ freqin     : num [1:495] 3 -2 3 1 -2 3 3 2 3 3 ...
 $ freqtt     : num [1:495] -2 -2 -2 1 -2 -2 -2 -2 -2 -2 ...
 $ freqyt     : num [1:495] -2 -2 2 2 -2 -2 -2 2 2 3 ...
 $ expvk      : num [1:495] 0 -2 4 3 5 3 5 4 3 3 ...
 $ expfb      : num [1:495] -2 -2 3 3 4 -2 -2 2 -2 2 ...
 $ exptw      : num [1:495] -2 -2 2 -2 -2 -2 -2 -2 -2 -2 ...
 $ expin      : num [1:495] 0 -2 4 4 -2 4 5 2 2 4 ...
 $ exptt      : num [1:495] -2 -2 -2 4 -2 -2 -2 -2 -2 -2 ...
 $ expyt      : num [1:495] -2 -2 3 4 -2 -2 -2 4 2 3 ...
 $ dighelp    : num [1:495] 1 0 1 1 1 1 1 1 1 1 ...
 $ siri       : num [1:495] 0 -2 0 1 0 0 1 0 1 0 ...
  [list output truncated]
 - attr(*, "spec")=
  .. cols(
  ..   id = col_character(),
  ..   e_dighelp = col_double(),
  ..   n_dighelp = col_double(),
  ..   e_socnet = col_double(),
  ..   f_socnet = col_double(),
  ..   n_socnet = col_double(),
  ..   gt_score = col_double(),
  ..   pr01 = col_double(),
  ..   pr02 = col_double(),
  ..   pr03 = col_double(),
  ..   pr04 = col_double(),
  ..   pr05 = col_double(),
  ..   pr06 = col_double(),
  ..   pr07 = col_double(),
  ..   pr08 = col_double(),
  ..   pr09 = col_double(),
  ..   pr10 = col_double(),
  ..   co01 = col_double(),
  ..   co02 = col_double(),
  ..   co03 = col_double(),
  ..   co04 = col_double(),
  ..   co05 = col_double(),
  ..   co06 = col_double(),
  ..   co07 = col_double(),
  ..   co08 = col_double(),
  ..   co09 = col_double(),
  ..   co10 = col_double(),
  ..   ut01 = col_double(),
  ..   ut02 = col_double(),
  ..   ut03 = col_double(),
  ..   ut04 = col_double(),
  ..   ut05 = col_double(),
  ..   ut06 = col_double(),
  ..   ut07 = col_double(),
  ..   ut08 = col_double(),
  ..   ut09 = col_double(),
  ..   ut10 = col_double(),
  ..   ut11 = col_double(),
  ..   ut12 = col_double(),
  ..   fa01 = col_double(),
  ..   fa02 = col_double(),
  ..   fa03 = col_double(),
  ..   fa04 = col_double(),
  ..   fa05 = col_double(),
  ..   fa06 = col_double(),
  ..   fa07 = col_double(),
  ..   fa08 = col_double(),
  ..   fa09 = col_double(),
  ..   fa10 = col_double(),
  ..   de01 = col_double(),
  ..   de02 = col_double(),
  ..   de03 = col_double(),
  ..   de04 = col_double(),
  ..   de05 = col_double(),
  ..   de06 = col_double(),
  ..   de07 = col_double(),
  ..   de08 = col_double(),
  ..   de09 = col_double(),
  ..   de10 = col_double(),
  ..   de11 = col_double(),
  ..   un01 = col_double(),
  ..   un02 = col_double(),
  ..   un03 = col_double(),
  ..   un04 = col_double(),
  ..   un05 = col_double(),
  ..   un06 = col_double(),
  ..   un07 = col_double(),
  ..   un08 = col_double(),
  ..   un09 = col_double(),
  ..   un10 = col_double(),
  ..   un11 = col_double(),
  ..   un12 = col_double(),
  ..   gt01 = col_double(),
  ..   gt02 = col_double(),
  ..   gt03 = col_double(),
  ..   gt04 = col_double(),
  ..   gt05 = col_double(),
  ..   gt06 = col_double(),
  ..   socnet = col_double(),
  ..   vk = col_double(),
  ..   fb = col_double(),
  ..   tw = col_double(),
  ..   `in` = col_double(),
  ..   tt = col_double(),
  ..   yt = col_double(),
  ..   freqvk = col_double(),
  ..   freqfb = col_double(),
  ..   freqtw = col_double(),
  ..   freqin = col_double(),
  ..   freqtt = col_double(),
  ..   freqyt = col_double(),
  ..   expvk = col_double(),
  ..   expfb = col_double(),
  ..   exptw = col_double(),
  ..   expin = col_double(),
  ..   exptt = col_double(),
  ..   expyt = col_double(),
  ..   dighelp = col_double(),
  ..   siri = col_double(),
  ..   alice = col_double(),
  ..   salut = col_double(),
  ..   oleg = col_double(),
  ..   alex = col_double(),
  ..   mia = col_double(),
  ..   mts = col_double(),
  ..   ggle = col_double(),
  ..   oth = col_double(),
  ..   oth_text = col_character(),
  ..   expsiri = col_double(),
  ..   expalice = col_double(),
  ..   expsalut = col_double(),
  ..   expoleg = col_double(),
  ..   expalex = col_double(),
  ..   expmia = col_double(),
  ..   expmts = col_double(),
  ..   expggle = col_double(),
  ..   expoth = col_double(),
  ..   expoth_text = col_character(),
  ..   selfdrcar = col_double(),
  ..   selfdrexp = col_double(),
  ..   selfdrsafe = col_double(),
  ..   eduai = col_double(),
  ..   eduaiexp = col_double(),
  ..   age = col_double(),
  ..   sex = col_character(),
  ..   edulvl1 = col_character(),
  ..   spec1 = col_character(),
  ..   edu2 = col_double(),
  ..   edulvl2 = col_character(),
  ..   spec2 = col_character(),
  ..   jobfield = col_character(),
  ..   jobpos = col_character(),
  ..   city = col_character()
  .. )

Preparation

Vectors of TAIA items:

pr_items <- colnames(taia)[8:17]
co_items <- colnames(taia)[18:27]
ut_items <- colnames(taia)[28:39]
fa_items <- colnames(taia)[40:49]
de_items <- colnames(taia)[50:60]
un_items <- colnames(taia)[61:72]
taia_items <- colnames(taia)[8:72]

Vector of GT items:

gt_items <- colnames(taia)[73:78]

Column names for further formatting:

col_names <- c("", "Num. of obs.", "Mean", "SD",
               "Median", "Trimmed Mean", "MAD",
               "Min", "Max", "Range",
               "Skewness", "Kurtuosis", "SE")
total_colnames <- c("Alpha", "Standardized Alpha", "Guttman's Lambda 6",
                    "Average interitem correlation", "S/N",
                    "Alpha SE", "Scale Mean", "Total Score SD",
                    "Median interitem correlation")
item_stats_colnames <- c("Num. of Obs.", "Discrimination",
                         "Std Cor",
                         "Cor Overlap Corrected",
                         "Cor if drop",
                         "Difficulty", "SD")
alpha_drop_colnames <- c("Alpha", "Standardized Alpha",
                "Guttman's Lambda 6",   "Average interitem correlation",
                "S/N",  "Alpha SE", "Var(r)","Median interitem correlation")

Exploratory analysis

TAIA descriptive statistics

taia %>% 
  select(all_of(pr_items)) %>% 
  describe() %>% 
  kable(caption = "Predictability", label = 1, digits = 2, col.names = col_names)

Table 1: Predictability

		Num. of obs.	Mean	SD	Median	Trimmed Mean	MAD	Min	Max	Range	Skewness	Kurtuosis	SE
pr01	1	495	2.84	0.99	3	2.87	1.48	0	5	5	-0.28	0.37	0.04
pr02	2	495	2.73	0.97	3	2.77	1.48	0	5	5	-0.19	0.10	0.04
pr03	3	495	2.89	1.01	3	2.91	1.48	0	5	5	-0.15	-0.05	0.05
pr04	4	495	2.84	1.04	3	2.87	1.48	0	5	5	-0.18	-0.04	0.05
pr05	5	495	2.22	1.20	2	2.22	1.48	0	5	5	0.03	-0.31	0.05
pr06	6	495	3.04	1.07	3	3.06	1.48	0	5	5	-0.26	0.07	0.05
pr07	7	495	2.59	1.11	3	2.61	1.48	0	5	5	-0.15	-0.10	0.05
pr08	8	495	3.05	0.91	3	3.09	0.00	0	5	5	-0.56	1.26	0.04
pr09	9	495	2.89	0.95	3	2.94	0.00	0	5	5	-0.50	1.05	0.04
pr10	10	495	2.83	1.04	3	2.90	1.48	0	5	5	-0.41	0.28	0.05

taia %>% select(all_of(pr_items)) %>% 
  pivot_longer(cols = all_of(pr_items)) %>% 
  ggplot(aes(value)) +
  geom_bar(fill = "darkred") +
  facet_wrap(~ name) +
  scale_x_discrete(limits = 0:5) +
  labs(x = "Score", y = "Number of observations",
       title = "Predictability") +
  theme(plot.title = element_text(hjust = .5))

• pr01 OK
  • Я считаю, что интеллектуальные системы надежны
• pr02 OK
  • Я считаю, что результаты работы интеллектуальных систем хорошо предсказуемы
• pr03 OK
  • Я считаю, что интеллектуальные системы ненадежны (R)
• pr04 OK
  • Я считаю, что результаты работы интеллектуальных систем невозможно предсказать (R)
• pr05 positive skewness
  • Я считаю, что поездки в машине, управляемой искусственным интеллектом, безопаснее, чем в обычной
• pr06 OK
  • Я считаю, что медицинская диагностика с применением интеллектуальных систем надеждее, чем без них
• pr07 OK
  • Я считаю, что финансовые операции под контролем искусственного интеллекта безопаснее, чем обычные
• pr08 high kurtosis
  • Я считаю, что интеллектуальные системы, обеспечивающие безопасность домов, хорошо справляются со своей задачей
• pr09 high kurtosis
  • Я считаю, что рекомендательные системы чаще всего правильно определяют предпочтения пользователей
• pr10 OK

taia %>% 
  select(all_of(co_items)) %>% 
  describe() %>% 
  kable(caption = "Consistency", label = 2, digits = 2, col.names = col_names)

Table 2: Consistency

		Num. of obs.	Mean	SD	Median	Trimmed Mean	MAD	Min	Max	Range	Skewness	Kurtuosis	SE
co01	1	495	2.49	1.08	3	2.51	1.48	0	5	5	-0.17	0.13	0.05
co02	2	495	2.51	1.04	3	2.53	1.48	0	5	5	-0.19	-0.06	0.05
co03	3	495	2.86	1.02	3	2.92	1.48	0	5	5	-0.40	0.31	0.05
co04	4	495	3.47	1.09	4	3.54	1.48	0	5	5	-0.57	0.32	0.05
co05	5	495	2.20	1.11	2	2.17	1.48	0	5	5	0.10	-0.17	0.05
co06	6	495	2.52	1.11	3	2.53	1.48	0	5	5	-0.13	-0.15	0.05
co07	7	495	1.59	1.13	2	1.52	1.48	0	5	5	0.54	0.12	0.05
co08	8	495	1.90	1.04	2	1.86	1.48	0	5	5	0.40	0.28	0.05
co09	9	495	2.05	1.07	2	2.01	1.48	0	5	5	0.35	0.12	0.05
co10	10	495	2.44	1.10	2	2.44	1.48	0	5	5	-0.04	-0.06	0.05

taia %>% select(all_of(co_items)) %>% 
  pivot_longer(cols = all_of(co_items)) %>% 
  ggplot(aes(value)) +
  geom_bar(fill = "chocolate3") +
  facet_wrap(~ name) +
  scale_x_discrete(limits = 0:5) +
  labs(x = "Score", y = "Number of observations",
       title = "Consistency") +
  theme(plot.title = element_text(hjust = .5))

• co01 OK
  • Интеллектуальные системы надежны, так как те системы, с которыми я сталкивался (сталкивалась), были надежными
• co02 OK
  • Я считаю, что если система при тестировании работает корректно, то и дальше она будет работать корректно
• co03 high kurtosis
  • Я считаю, что интеллектуальные системы совершают меньше технических ошибок, чем люди
• co04 high negative skewness
  • Со временем любая интеллектуальная система будет совершать всё меньше ошибок
• co05 positive skewness
  • Если интеллектуальные системы, с которыми я сталкивался (сталкивалась), были надежными, то я могу считать надёжными другие системы
• co06 positive skewness
  • Я могу судить о надёжности новой интеллектуальной системы по опыту работы с другими системами
• co07 high positive skewness
  • Я могу сказать, что система работает корректно, только протестировав её (R)
• co08 positive skewness
  • Если одна интеллектуальная система подводит меня, то и с другими будет то же самое
• co09positive skewness
  • Если одна интеллектуальная система соответствует моим ожиданиям, то с другими будет то же самое
• co10 positive skewness
  • Я могу сформировать ожидания относительно работы интеллектуальных систем в целом на основе опыта взаимодействия с одной системой

taia %>% 
  select(all_of(ut_items)) %>% 
  describe() %>% 
  kable(caption = "Utility", label = 3, digits = 2, col.names = col_names)

Table 3: Utility

		Num. of obs.	Mean	SD	Median	Trimmed Mean	MAD	Min	Max	Range	Skewness	Kurtuosis	SE
ut01	1	495	3.78	1.05	4	3.88	1.48	0	5	5	-0.86	1.12	0.05
ut02	2	495	3.52	1.05	3	3.59	1.48	0	5	5	-0.53	0.50	0.05
ut03	3	495	3.56	1.11	4	3.64	1.48	0	5	5	-0.57	0.15	0.05
ut04	4	495	3.09	1.11	3	3.15	1.48	0	5	5	-0.43	0.03	0.05
ut05	5	495	3.05	1.21	3	3.09	1.48	0	5	5	-0.33	-0.15	0.05
ut06	6	495	3.27	1.10	3	3.31	1.48	0	5	5	-0.61	0.68	0.05
ut07	7	495	3.20	1.13	3	3.23	1.48	0	5	5	-0.28	-0.22	0.05
ut08	8	495	3.44	1.05	3	3.49	1.48	0	5	5	-0.55	0.44	0.05
ut09	9	495	3.18	1.17	3	3.23	1.48	0	5	5	-0.47	0.16	0.05
ut10	10	495	2.17	1.11	2	2.16	1.48	0	5	5	0.08	-0.23	0.05
ut11	11	495	2.67	1.23	3	2.69	1.48	0	5	5	-0.11	-0.41	0.06
ut12	12	495	3.16	1.15	3	3.21	1.48	0	5	5	-0.42	0.03	0.05

taia %>% select(all_of(ut_items)) %>% 
  pivot_longer(cols = all_of(ut_items)) %>% 
  ggplot(aes(value)) +
  geom_bar(fill = "goldenrod3") +
  facet_wrap(~ name) +
  scale_x_discrete(limits = 0:5) +
  labs(x = "Score", y = "Number of observations",
       title = "Utility") +
  theme(plot.title = element_text(hjust = .5))

• ut01 extremely high negative skewness
  • Я считаю, что интеллектуальные технологии — неотъемлемая часть развития общества
• ut02 high negative skewness
  • Я считаю, что человечество нуждается в интеллектуальных системах
• ut03 high negative skewness
  • Мне кажется, человечеству будет лучше без интеллектуальных систем (R)
• ut04 negative skewness
  • Я считаю, что развитие интеллектуальных систем — это оправданный риск для общества
• ut05 OK
  • По моему мнению, без интеллектуальных систем общественный прогресс остановился бы
• ut06 negative skewness
  • Я считаю, что интеллектуальные системы существенно повышают качество медицинской диагностики
• ut07 light negative skewness
  • Мне кажется, что оформить услуги с цифровыми помощниками гораздо проще, чем без них
• ut08 negative skewness
  • Мне кажется, рекомендательные сервисы существенно сокращают время поиска нужной информации
• ut09 negative skewness
  • Я считаю, что если полиция будет использовать интеллектуальные системы, то количество раскрытых преступлений увеличится
• ut10 positive skewness
  • Мне кажется, при оформлении услуг через интернет можно справиться и без цифровых помощников (R)
• ut11 OK
  • Я считаю, что если на дорогах появятся машины, управляемые искусственным интеллектом, то число аварий снизится
• ut12 negative skewness
  • Я считаю, что использование интеллектуальных систем в обучении повышает качество образования

taia %>% 
  select(all_of(fa_items)) %>% 
  describe() %>% 
  kable(caption = "Faith", label = 4, digits = 2, col.names = col_names)

Table 4: Faith

		Num. of obs.	Mean	SD	Median	Trimmed Mean	MAD	Min	Max	Range	Skewness	Kurtuosis	SE
fa01	1	495	2.42	1.10	2	2.42	1.48	0	5	5	-0.02	-0.29	0.05
fa02	2	495	2.16	1.18	2	2.15	1.48	0	5	5	0.18	-0.42	0.05
fa03	3	495	1.51	1.13	1	1.42	1.48	0	5	5	0.66	0.16	0.05
fa04	4	495	1.57	1.08	1	1.51	1.48	0	5	5	0.55	0.17	0.05
fa05	5	495	2.46	1.10	2	2.48	1.48	0	5	5	-0.15	-0.10	0.05
fa06	6	495	2.47	1.08	3	2.49	1.48	0	5	5	-0.18	0.06	0.05
fa07	7	495	2.37	1.09	2	2.38	1.48	0	5	5	-0.14	-0.17	0.05
fa08	8	495	2.21	1.14	2	2.17	1.48	0	5	5	0.28	-0.13	0.05
fa09	9	495	2.29	1.18	2	2.27	1.48	0	5	5	0.15	-0.40	0.05
fa10	10	495	2.64	1.20	3	2.62	1.48	0	5	5	0.06	-0.28	0.05

taia %>% select(all_of(fa_items)) %>% 
  pivot_longer(cols = all_of(fa_items)) %>% 
  ggplot(aes(value)) +
  geom_bar(fill = "darkgreen") +
  facet_wrap(~ name) +
  scale_x_discrete(limits = 0:5) +
  labs(x = "Score", y = "Number of observations",
       title = "Faith") +
  theme(plot.title = element_text(hjust = .5))

• fa01 OK
  • Я готов (готова) довериться интеллектуальным системам, даже если я не до конца понимаю, как они работают
• fa02 light positive skewness
  • Чтобы доверять интеллектуальной системе, мне нужно точно понимать, как работают её алгоритмы (R)
• fa03 hard positive skewness
  • Если интеллектуальная система перестает реагировать на запросы, мне с этим комфортно
• fa04 hard positive skewness
  • Если интеллектуальная система управлениями финансами не реагирует на запросы, я все равно буду уверен, что она работает корректно
• fa05 OK
  • Я готов (готова) доверять результатам работы интеллектуальных систем, даже если я не знаю, как они работают
• fa06 OK
  • Я готов (готова) довериться работе интеллектуальных систем так же, как работе профессионалов
• fa07 OK
  • Я предпочту сам (сама) контролировать весь процесс нежели дам контроль интеллектуальной системе (R)
• fa08 light positive skewness
  • Мне нужно знать детали работы алгоритма, чтобы быть уверенным (уверенной) в качестве результата его работы (R)
• fa09 OK
  • Если я не понимаю, как работает интеллектуальная система, я не могу быть уверенным (уверенной) в результате её работы (R)
• fa10 OK
  • Мне не важно, как работает интеллектуальная система, если она должным образом справляется со своей задачей

taia %>% 
  select(all_of(de_items)) %>% 
  describe() %>% 
  kable(caption = "Dependability", label = 5, digits = 2, col.names = col_names)

Table 5: Dependability

		Num. of obs.	Mean	SD	Median	Trimmed Mean	MAD	Min	Max	Range	Skewness	Kurtuosis	SE
de01	1	495	2.59	1.10	3	2.64	1.48	0	5	5	-0.42	0.08	0.05
de02	2	495	2.17	1.15	2	2.18	1.48	0	5	5	0.00	-0.34	0.05
de03	3	495	2.17	1.19	2	2.17	1.48	0	5	5	0.04	-0.30	0.05
de04	4	495	1.90	1.05	2	1.85	1.48	0	5	5	0.55	0.66	0.05
de05	5	495	3.57	1.16	4	3.68	1.48	0	5	5	-0.78	0.48	0.05
de06	6	495	2.23	1.23	2	2.25	1.48	0	5	5	0.01	-0.43	0.06
de07	7	495	2.82	1.00	3	2.86	1.48	0	5	5	-0.30	0.31	0.04
de08	8	495	2.65	1.06	3	2.70	1.48	0	5	5	-0.40	0.14	0.05
de09	9	495	3.44	1.20	4	3.54	1.48	0	5	5	-0.61	-0.14	0.05
de10	10	495	2.25	1.18	2	2.28	1.48	0	5	5	-0.22	-0.42	0.05
de11	11	495	2.31	1.20	2	2.31	1.48	0	5	5	0.00	-0.52	0.05

taia %>% select(all_of(de_items)) %>% 
  pivot_longer(cols = all_of(de_items)) %>% 
  ggplot(aes(value)) +
  geom_bar(fill = "darkblue") +
  facet_wrap(~ name) +
  scale_x_discrete(limits = 0:5) +
  labs(x = "Score", y = "Number of observations",
       title = "Dependability") +
  theme(plot.title = element_text(hjust = .5))

• de01 negative skewness
  • Я готов (готова) следовать рекомендациям рекомендательных систем социальных сетей
• de02 OK
  • Я готов (готова) делегировать управление финансами интеллектуальному помощнику
• de03 OK
  • Если интеллектуальная система запрашивает мои личные данные, я могу быть уверен (уверенна) в их сохранности
• de04 hard positive skewness
  • Я могу доверять интеллектуальной системе, если я точно понимаю, какие опасности исходят от неё
• de05 hard negative skewness
  • Я бы мог (могла) жить в «умном доме»
• de06 negative kurtosis
  • Если бы я ехал (ехала) в автомобиле, управляемом искусственным интеллектом, я бы был спокоен за свою безопасность
• de07 OK
  • Если меня обследуют с помощью интеллектуальных медицинских технологий, я могу доверять выставленному диагнозу
• de08 OK
  • Я считаю, что при покупках с интеллектуальными помощниками риск ошибиться меньше, чем без них
• de09 negative skewness
  • Мне было бы некомфортно жить в «умном доме» (R)
• de10 negative kurtosis
  • Я могу доверить искусственному интеллекту задачи, от которых зависит моя личная безопасность
• de11 negative kurtosis
  • Я могу доверить искусственному интеллекту только рутинные задачи (например, уборка) (R)

taia %>%
  select(all_of(un_items)) %>% 
  describe() %>% 
  kable(caption = "Understanding", label = 6, digits = 2, col.names = col_names)

Table 6: Understanding

		Num. of obs.	Mean	SD	Median	Trimmed Mean	MAD	Min	Max	Range	Skewness	Kurtuosis	SE
un01	1	495	2.93	1.05	3	3.01	1.48	0	5	5	-0.48	0.31	0.05
un02	2	495	2.47	1.14	3	2.49	1.48	0	5	5	-0.17	-0.27	0.05
un03	3	495	3.02	1.17	3	3.10	1.48	0	5	5	-0.55	0.01	0.05
un04	4	495	2.61	1.09	3	2.65	1.48	0	5	5	-0.33	-0.22	0.05
un05	5	495	2.82	1.10	3	2.90	1.48	0	5	5	-0.51	0.24	0.05
un06	6	495	2.29	1.23	2	2.26	1.48	0	5	5	0.19	-0.62	0.06
un07	7	495	2.13	1.18	2	2.14	1.48	0	5	5	-0.02	-0.54	0.05
un08	8	495	2.90	1.16	3	2.96	1.48	0	5	5	-0.45	0.00	0.05
un09	9	495	2.32	1.23	2	2.37	1.48	0	5	5	-0.18	-0.75	0.06
un10	10	495	2.24	1.15	2	2.23	1.48	0	5	5	0.05	-0.44	0.05
un11	11	495	2.63	1.20	3	2.66	1.48	0	5	5	-0.25	-0.37	0.05
un12	12	495	2.89	1.12	3	2.96	1.48	0	5	5	-0.46	0.13	0.05

taia %>% select(all_of(un_items)) %>% 
  pivot_longer(cols = all_of(un_items)) %>% 
  ggplot(aes(value)) +
  geom_bar(fill = "purple4") +
  facet_wrap(~ name) +
  scale_x_discrete(limits = 0:5) +
  labs(x = "Score", y = "Number of observations",
       title = "Understanding") +
  theme(plot.title = element_text(hjust = .5))

• un01 OK
  • Я понимаю, как происходит взаимодействие человека с интеллектуальными системами
• un02 OK
  • Я понимаю, как работают алгоритмы интеллектуальных систем
• un03 negative skewness
  • Я стараюсь разобраться в том, как работают интеллектуальные системы
• un04 negative skewness
  • Я понимаю, как работают отдельные элементы интеллектуальных систем
• un05 positive kurtosis
  • Я понимаю общий принцип работы интеллектуальных систем
• un06 negative kurtosis
  • Я плохо разбираюсь в тонкостях работы интеллектуальных систем (R)
• un07 negative kurtosis
  • Мне понятно, как работают интеллектуальные алгоритмы, применяемые в медицинской диагностике
• un08 OK
  • Мне понятно, как работают алгоритмы рекомендательных систем социальных сетей
• un09 extra negative kurtosis
  • Я понимаю, как работают алгоритмы автомобилей, управляемых искусственным интеллектом
• un10 negative kurtosis
  • Я понимаю, как работают алгоритмы интеллектуальных систем, которые управляют финансами
• un11 OK
  • Мне понятно, как устроены алгоритмы машинного перевода текстов
• un12 OK
  • Мне понятно, как работают алгоритмы систем типа «умный дом»

Correlations

Predictability

corrplot.mixed(cor(taia %>% select(all_of(pr_items))),
               lower.col = "black")

Consistency

corrplot.mixed(cor(taia %>% select(all_of(co_items))),
               lower.col = "black")

Utility

corrplot.mixed(cor(taia %>% select(all_of(ut_items))),
               lower.col = "black")

Faith

corrplot.mixed(cor(taia %>% select(all_of(fa_items))),
               lower.col = "black")

Dependability

corrplot.mixed(cor(taia %>% select(all_of(de_items))),
               lower.col = "black")

Understanding

corrplot.mixed(cor(taia %>% select(all_of(un_items))),
               lower.col = "black")

All TAIA items correlations

qgraph::qgraph(
  cor(taia %>% select(all_of(taia_items))),
  layout = "spring",
  posCol = "darkgreen",
  negCol = "darkred"
)

Psychometric Analysis

Subscales

Predictability

pr1 <- psych::alpha(
  taia %>% select(all_of(pr_items)),
  cumulative = TRUE,
  title = "Predictability Factor",
  check.keys = FALSE
)

kable(pr1$total,
      caption = "Perdictability. Subscale statistics", 
      label = 7, digits = 2,
      col.names = total_colnames
      )

Table 7: Perdictability. Subscale statistics

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Scale Mean	Total Score SD	Median interitem correlation
	0.81	0.81	0.82	0.3	4.25	0.01	27.92	6.23	0.33

pr1$item.stats$mean <- pr1$item.stats$mean / 5
kable(pr1$item.stats,
      caption = "Predictability. Items statistics",
      label = 8, digits = 2,
      col.names = item_stats_colnames)

Table 8: Predictability. Items statistics

	Num. of Obs.	Discrimination	Std Cor	Cor Overlap Corrected	Cor if drop	Difficulty	SD
pr01	495	0.79	0.80	0.80	0.72	0.57	0.99
pr02	495	0.66	0.66	0.62	0.56	0.55	0.97
pr03	495	0.45	0.45	0.37	0.31	0.58	1.01
pr04	495	0.32	0.32	0.21	0.16	0.57	1.04
pr05	495	0.61	0.59	0.51	0.46	0.44	1.20
pr06	495	0.62	0.62	0.56	0.50	0.61	1.07
pr07	495	0.74	0.73	0.70	0.63	0.52	1.11
pr08	495	0.72	0.73	0.71	0.64	0.61	0.91
pr09	495	0.61	0.62	0.56	0.50	0.58	0.95
pr10	495	0.55	0.56	0.47	0.42	0.57	1.04

pr1$item.stats %>%
  ggplot(aes(x = row.names(pr1$item.stats))) +
  geom_point(aes(y = mean), color = "darkblue", size = 3) +
  geom_point(aes(y = raw.r), color = "darkred", size = 2) +
  geom_hline(yintercept = 0.1, color = "darkblue") +
  geom_hline(yintercept = 0.9, color = "darkblue") +
  geom_hline(yintercept = 0.25, color = "darkred") +
  geom_hline(yintercept = 0, color = "black") +
  labs(x = "Item", y = "Value",
       title = "Predictability. Items characteristics",
       subtitle = "Difficulty (blue) and Dicrimination (red)") +
  theme(plot.title = element_text(hjust = .5),
        plot.subtitle = element_text(hjust = .5))

kable(pr1$alpha.drop,
      caption = "Predictability. Subscale statistics when item drop",
      label = 9, digits = 2, col.names = alpha_drop_colnames)

Table 9: Predictability. Subscale statistics when item drop

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Var(r)	Median interitem correlation
pr01	0.76	0.77	0.78	0.27	3.27	0.02	0.02	0.29
pr02	0.78	0.79	0.80	0.29	3.66	0.01	0.03	0.32
pr03	0.81	0.81	0.81	0.32	4.33	0.01	0.03	0.36
pr04	0.82	0.83	0.82	0.35	4.78	0.01	0.02	0.36
pr05	0.79	0.80	0.81	0.30	3.88	0.01	0.03	0.33
pr06	0.79	0.79	0.81	0.30	3.79	0.01	0.03	0.33
pr07	0.77	0.78	0.79	0.28	3.46	0.02	0.02	0.30
pr08	0.77	0.78	0.79	0.28	3.46	0.02	0.02	0.30
pr09	0.79	0.79	0.80	0.30	3.80	0.01	0.03	0.35
pr10	0.80	0.80	0.81	0.31	3.99	0.01	0.03	0.35

kable(pr1$response.freq,
      caption = "Predictability. Non missing response frequency for each item",
      label = 10, digits = 2)

Table 10: Predictability. Non missing response frequency for each item

	0	1	2	3	4	5	miss
pr01	0.02	0.06	0.24	0.45	0.19	0.04	0
pr02	0.01	0.08	0.28	0.43	0.17	0.03	0
pr03	0.01	0.06	0.26	0.40	0.22	0.05	0
pr04	0.02	0.07	0.27	0.38	0.21	0.05	0
pr05	0.09	0.17	0.33	0.29	0.09	0.03	0
pr06	0.02	0.06	0.20	0.41	0.23	0.08	0
pr07	0.04	0.12	0.28	0.38	0.14	0.04	0
pr08	0.02	0.03	0.16	0.52	0.24	0.04	0
pr09	0.02	0.05	0.18	0.53	0.17	0.04	0
pr10	0.02	0.08	0.21	0.45	0.20	0.04	0

Consistency

co1 <- psych::alpha(
  taia %>% select(all_of(co_items)),
  cumulative = TRUE,
  title = "Consistency Factor",
  check.keys = FALSE
)

Some items ( co07 ) were negatively correlated with the total scale and 
probably should be reversed.  
To do this, run the function again with the 'check.keys=TRUE' option

kable(co1$total,
      caption = "Consistency. Subscale statistics", 
      label = 11, digits = 2,
      col.names = total_colnames)

Table 11: Consistency. Subscale statistics

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Scale Mean	Total Score SD	Median interitem correlation
	0.76	0.77	0.8	0.25	3.27	0.01	24.03	6.1	0.27

co1$item.stats$mean <- co1$item.stats$mean / 5
kable(co1$item.stats,
      caption = "Consistency. Items statistics",
      label = 12, digits = 2,
      col.names = item_stats_colnames)

Table 12: Consistency. Items statistics

	Num. of Obs.	Discrimination	Std Cor	Cor Overlap Corrected	Cor if drop	Difficulty	SD
co01	495	0.74	0.74	0.72	0.64	0.50	1.08
co02	495	0.68	0.69	0.65	0.57	0.50	1.04
co03	495	0.55	0.55	0.48	0.41	0.57	1.02
co04	495	0.40	0.41	0.30	0.24	0.69	1.09
co05	495	0.79	0.78	0.79	0.70	0.44	1.11
co06	495	0.65	0.65	0.61	0.53	0.50	1.11
co07	495	-0.03	-0.04	-0.22	-0.22	0.32	1.13
co08	495	0.45	0.46	0.36	0.30	0.38	1.04
co09	495	0.76	0.77	0.76	0.67	0.41	1.07
co10	495	0.67	0.67	0.62	0.56	0.49	1.10

co1$item.stats %>%
  ggplot(aes(x = row.names(co1$item.stats))) +
  geom_point(aes(y = mean), color = "darkblue", size = 3) +
  geom_point(aes(y = raw.r), color = "darkred", size = 2) +
  geom_hline(yintercept = 0.1, color = "darkblue") +
  geom_hline(yintercept = 0.9, color = "darkblue") +
  geom_hline(yintercept = 0.25, color = "darkred") +
  geom_hline(yintercept = 0, color = "black") +
  labs(x = "Item", y = "Value",
       title = "Consistency. Items characteristics",
       subtitle = "Difficulty (blue) and Dicrimination (red)") +
  theme(plot.title = element_text(hjust = .5),
        plot.subtitle = element_text(hjust = .5))

kable(co1$alpha.drop,
      caption = "Consistency. Subscale statistics when item drop",
      label = 13, digits = 2,
      col.names = alpha_drop_colnames)

Table 13: Consistency. Subscale statistics when item drop

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Var(r)	Median interitem correlation
co01	0.71	0.72	0.76	0.22	2.52	0.02	0.06	0.26
co02	0.72	0.73	0.77	0.23	2.66	0.02	0.06	0.26
co03	0.74	0.75	0.79	0.25	2.98	0.02	0.07	0.27
co04	0.77	0.77	0.80	0.27	3.36	0.01	0.06	0.35
co05	0.70	0.71	0.75	0.21	2.42	0.02	0.06	0.26
co06	0.73	0.73	0.77	0.23	2.74	0.02	0.06	0.27
co07	0.83	0.82	0.83	0.34	4.70	0.01	0.03	0.36
co08	0.76	0.76	0.79	0.26	3.23	0.02	0.07	0.34
co09	0.71	0.71	0.75	0.22	2.47	0.02	0.06	0.26
co10	0.72	0.73	0.77	0.23	2.69	0.02	0.07	0.26

kable(co1$response.freq,
      caption = "Consistency. Non missing response frequency for each item",
      label = 14, digits = 2)

Table 14: Consistency. Non missing response frequency for each item

	0	1	2	3	4	5	miss
co01	0.05	0.11	0.31	0.39	0.11	0.03	0
co02	0.03	0.12	0.32	0.38	0.13	0.02	0
co03	0.02	0.07	0.22	0.44	0.21	0.04	0
co04	0.01	0.04	0.10	0.35	0.32	0.18	0
co05	0.06	0.19	0.37	0.27	0.09	0.02	0
co06	0.04	0.14	0.28	0.38	0.13	0.03	0
co07	0.18	0.31	0.32	0.14	0.04	0.02	0
co08	0.08	0.27	0.42	0.16	0.06	0.01	0
co09	0.06	0.24	0.40	0.22	0.06	0.02	0
co10	0.04	0.14	0.33	0.34	0.11	0.03	0

Utility

ut1 <- psych::alpha(
  taia %>% select(all_of(ut_items)),
  cumulative = TRUE,
  title = "Utility Factor",
  check.keys = FALSE
)

kable(ut1$total,
      caption = "Utility. Subscale statistics", 
      label = 15, digits = 2,
      col.names = total_colnames)

Table 15: Utility. Subscale statistics

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Scale Mean	Total Score SD	Median interitem correlation
	0.86	0.86	0.87	0.34	6.17	0.01	38.09	8.44	0.37

ut1$item.stats$mean <- ut1$item.stats$mean / 5
kable(ut1$item.stats,
      caption = "Utility. Items statistics",
      label = 16, digits = 2,
      col.names = item_stats_colnames)

Table 16: Utility. Items statistics

	Num. of Obs.	Discrimination	Std Cor	Cor Overlap Corrected	Cor if drop	Difficulty	SD
ut01	495	0.77	0.78	0.78	0.71	0.76	1.05
ut02	495	0.82	0.83	0.84	0.77	0.70	1.05
ut03	495	0.57	0.57	0.52	0.47	0.71	1.11
ut04	495	0.51	0.51	0.44	0.40	0.62	1.11
ut05	495	0.69	0.69	0.65	0.61	0.61	1.21
ut06	495	0.76	0.76	0.74	0.70	0.65	1.10
ut07	495	0.63	0.63	0.59	0.54	0.64	1.13
ut08	495	0.65	0.66	0.62	0.57	0.69	1.05
ut09	495	0.68	0.68	0.64	0.59	0.64	1.17
ut10	495	0.17	0.17	0.06	0.04	0.43	1.11
ut11	495	0.56	0.55	0.48	0.45	0.53	1.23
ut12	495	0.71	0.71	0.68	0.64	0.63	1.15

ut1$item.stats %>%
  ggplot(aes(x = row.names(ut1$item.stats))) +
  geom_point(aes(y = mean), color = "darkblue", size = 3) +
  geom_point(aes(y = raw.r), color = "darkred", size = 2) +
  geom_hline(yintercept = 0.1, color = "darkblue") +
  geom_hline(yintercept = 0.9, color = "darkblue") +
  geom_hline(yintercept = 0.25, color = "darkred") +
  geom_hline(yintercept = 0, color = "black") +
  labs(x = "Item", y = "Value",
       title = "Utility. Items characteristics",
       subtitle = "Difficulty (blue) and Dicrimination (red)") +
  theme(plot.title = element_text(hjust = .5),
        plot.subtitle = element_text(hjust = .5))

kable(ut1$alpha.drop,
      caption = "Utility. Subscale statistics when item drop",
      label = 17, digits = 2,
      col.names = alpha_drop_colnames)

Table 17: Utility. Subscale statistics when item drop

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Var(r)	Median interitem correlation
ut01	0.84	0.84	0.85	0.32	5.16	0.01	0.03	0.34
ut02	0.83	0.83	0.84	0.31	5.00	0.01	0.03	0.33
ut03	0.85	0.85	0.86	0.35	5.84	0.01	0.04	0.41
ut04	0.86	0.86	0.87	0.36	6.06	0.01	0.03	0.41
ut05	0.84	0.84	0.86	0.33	5.45	0.01	0.04	0.37
ut06	0.84	0.84	0.85	0.32	5.21	0.01	0.03	0.33
ut07	0.85	0.85	0.86	0.34	5.65	0.01	0.04	0.37
ut08	0.85	0.85	0.86	0.34	5.55	0.01	0.03	0.37
ut09	0.84	0.85	0.86	0.33	5.49	0.01	0.03	0.37
ut10	0.88	0.88	0.88	0.40	7.40	0.01	0.01	0.41
ut11	0.85	0.86	0.87	0.35	5.92	0.01	0.04	0.41
ut12	0.84	0.84	0.86	0.33	5.37	0.01	0.03	0.35

kable(ut1$response.freq,
      caption = "Utility. Non missing response frequency for each item",
      label = 18, digits = 2)

Table 18: Utility. Non missing response frequency for each item

	0	1	2	3	4	5	miss
ut01	0.01	0.01	0.06	0.29	0.34	0.28	0
ut02	0.01	0.02	0.09	0.38	0.30	0.20	0
ut03	0.01	0.04	0.09	0.33	0.31	0.22	0
ut04	0.02	0.08	0.15	0.40	0.27	0.09	0
ut05	0.03	0.06	0.20	0.35	0.23	0.12	0
ut06	0.03	0.03	0.13	0.39	0.30	0.12	0
ut07	0.01	0.05	0.19	0.35	0.26	0.14	0
ut08	0.01	0.03	0.11	0.36	0.34	0.15	0
ut09	0.03	0.05	0.15	0.38	0.25	0.13	0
ut10	0.07	0.19	0.37	0.26	0.09	0.02	0
ut11	0.05	0.12	0.27	0.32	0.18	0.07	0
ut12	0.02	0.07	0.15	0.38	0.26	0.12	0

Faith

fa1 <- psych::alpha(
  taia %>% select(all_of(fa_items)),
  cumulative = TRUE,
  title = "Faith Factor",
  check.keys = FALSE
)

kable(fa1$total,
      caption = "Faith. Subscale statistics", 
      label = 19, digits = 2,
      col.names = total_colnames)

Table 19: Faith. Subscale statistics

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Scale Mean	Total Score SD	Median interitem correlation
	0.77	0.77	0.81	0.25	3.26	0.02	22.1	6.41	0.24

fa1$item.stats$mean <- fa1$item.stats$mean / 5
kable(fa1$item.stats,
      caption = "Faith. Items statistics",
      label = 20, digits = 2,
      col.names = item_stats_colnames)

Table 20: Faith. Items statistics

	Num. of Obs.	Discrimination	Std Cor	Cor Overlap Corrected	Cor if drop	Difficulty	SD
fa01	495	0.76	0.76	0.76	0.67	0.48	1.10
fa02	495	0.61	0.60	0.56	0.47	0.43	1.18
fa03	495	0.27	0.28	0.16	0.10	0.30	1.13
fa04	495	0.41	0.42	0.33	0.26	0.31	1.08
fa05	495	0.77	0.78	0.78	0.69	0.49	1.10
fa06	495	0.55	0.56	0.50	0.42	0.49	1.08
fa07	495	0.42	0.42	0.31	0.26	0.47	1.09
fa08	495	0.58	0.57	0.52	0.44	0.44	1.14
fa09	495	0.66	0.65	0.62	0.53	0.46	1.18
fa10	495	0.63	0.62	0.57	0.50	0.53	1.20

fa1$item.stats %>%
  ggplot(aes(x = row.names(fa1$item.stats))) +
  geom_point(aes(y = mean), color = "darkblue", size = 3) +
  geom_point(aes(y = raw.r), color = "darkred", size = 2) +
  geom_hline(yintercept = 0.1, color = "darkblue") +
  geom_hline(yintercept = 0.9, color = "darkblue") +
  geom_hline(yintercept = 0.25, color = "darkred") +
  geom_hline(yintercept = 0, color = "black") +
  labs(x = "Item", y = "Value",
       title = "Faith. Items characteristics",
       subtitle = "Difficulty (blue) and Dicrimination (red)") +
  theme(plot.title = element_text(hjust = .5),
        plot.subtitle = element_text(hjust = .5))

kable(fa1$alpha.drop,
      caption = "Faith. Subscale statistics when item drop",
      label = 21, digits = 2,
      col.names = alpha_drop_colnames)

Table 21: Faith. Subscale statistics when item drop

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Var(r)	Median interitem correlation
fa01	0.71	0.71	0.76	0.22	2.47	0.02	0.04	0.22
fa02	0.74	0.74	0.78	0.24	2.87	0.02	0.04	0.24
fa03	0.79	0.79	0.82	0.29	3.70	0.01	0.04	0.30
fa04	0.77	0.77	0.81	0.27	3.30	0.02	0.04	0.26
fa05	0.71	0.71	0.76	0.21	2.43	0.02	0.04	0.22
fa06	0.75	0.75	0.79	0.25	2.95	0.02	0.05	0.29
fa07	0.77	0.77	0.81	0.27	3.30	0.02	0.05	0.30
fa08	0.74	0.75	0.79	0.25	2.92	0.02	0.04	0.24
fa09	0.73	0.73	0.78	0.23	2.73	0.02	0.04	0.24
fa10	0.74	0.74	0.79	0.24	2.79	0.02	0.04	0.24

kable(fa1$response.freq,
      caption = "Faith. Non missing response frequency for each item",
      label = 22, digits = 2)

Table 22: Faith. Non missing response frequency for each item

	0	1	2	3	4	5	miss
fa01	0.04	0.16	0.32	0.33	0.13	0.03	0
fa02	0.08	0.21	0.36	0.21	0.12	0.02	0
fa03	0.19	0.35	0.29	0.11	0.05	0.01	0
fa04	0.16	0.34	0.33	0.12	0.04	0.01	0
fa05	0.05	0.12	0.33	0.34	0.13	0.03	0
fa06	0.05	0.12	0.32	0.38	0.11	0.03	0
fa07	0.05	0.15	0.32	0.35	0.11	0.02	0
fa08	0.05	0.20	0.38	0.23	0.10	0.03	0
fa09	0.06	0.19	0.34	0.25	0.13	0.03	0
fa10	0.04	0.12	0.31	0.32	0.14	0.08	0

Dependability

de1 <- psych::alpha(
  taia %>% select(all_of(de_items)),
  cumulative = TRUE,
  title = "Dependability Factor",
  check.keys = FALSE
)

Some items ( de04 ) were negatively correlated with the total scale and 
probably should be reversed.  
To do this, run the function again with the 'check.keys=TRUE' option

kable(de1$total,
      caption = "Dependability. Subscale statistics", 
      label = 23, digits = 2,
      col.names = total_colnames)

Table 23: Dependability. Subscale statistics

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Scale Mean	Total Score SD	Median interitem correlation
	0.75	0.75	0.8	0.21	2.96	0.02	28.09	6.74	0.24

de1$item.stats$mean <- de1$item.stats$mean / 5
kable(de1$item.stats,
      caption = "Dependability. Items statistics",
      label = 24, digits = 2,
      col.names = item_stats_colnames)

Table 24: Dependability. Items statistics

	Num. of Obs.	Discrimination	Std Cor	Cor Overlap Corrected	Cor if drop	Difficulty	SD
de01	495	0.57	0.58	0.52	0.45	0.52	1.10
de02	495	0.72	0.72	0.69	0.61	0.43	1.15
de03	495	0.66	0.66	0.61	0.54	0.43	1.19
de04	495	-0.23	-0.22	-0.39	-0.36	0.38	1.05
de05	495	0.59	0.58	0.56	0.46	0.71	1.16
de06	495	0.67	0.67	0.62	0.55	0.45	1.23
de07	495	0.58	0.60	0.54	0.47	0.56	1.00
de08	495	0.67	0.68	0.66	0.57	0.53	1.06
de09	495	0.45	0.44	0.39	0.30	0.69	1.20
de10	495	0.74	0.74	0.72	0.64	0.45	1.18
de11	495	0.43	0.42	0.30	0.27	0.46	1.20

de1$item.stats %>%
  ggplot(aes(x = row.names(de1$item.stats))) +
  geom_point(aes(y = mean), color = "darkblue", size = 3) +
  geom_point(aes(y = raw.r), color = "darkred", size = 2) +
  geom_hline(yintercept = 0.1, color = "darkblue") +
  geom_hline(yintercept = 0.9, color = "darkblue") +
  geom_hline(yintercept = 0.25, color = "darkred") +
  geom_hline(yintercept = 0, color = "black") +
  labs(x = "Item", y = "Value",
       title = "Dependability. Items characteristics",
       subtitle = "Difficulty (blue) and Dicrimination (red)") +
  theme(plot.title = element_text(hjust = .5),
        plot.subtitle = element_text(hjust = .5))

kable(de1$alpha.drop,
      caption = "Dependability. Subscale statistics when item drop",
      label = 25, digits = 2,
      col.names = alpha_drop_colnames)

Table 25: Dependability. Subscale statistics when item drop

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Var(r)	Median interitem correlation
de01	0.73	0.72	0.78	0.21	2.59	0.02	0.07	0.22
de02	0.71	0.70	0.76	0.19	2.32	0.02	0.07	0.22
de03	0.72	0.71	0.77	0.20	2.44	0.02	0.07	0.23
de04	0.82	0.82	0.84	0.31	4.49	0.01	0.02	0.32
de05	0.73	0.72	0.76	0.21	2.59	0.02	0.07	0.22
de06	0.71	0.71	0.77	0.19	2.42	0.02	0.07	0.22
de07	0.73	0.72	0.78	0.20	2.56	0.02	0.07	0.22
de08	0.71	0.70	0.76	0.19	2.39	0.02	0.06	0.22
de09	0.75	0.74	0.78	0.22	2.88	0.02	0.07	0.30
de10	0.70	0.69	0.76	0.19	2.28	0.02	0.06	0.22
de11	0.75	0.75	0.80	0.23	2.93	0.02	0.08	0.32

kable(de1$response.freq,
      caption = "Dependability. Non missing response frequency for each item",
      label = 26, digits = 2)

Table 26: Dependability. Non missing response frequency for each item

	0	1	2	3	4	5	miss
de01	0.05	0.11	0.24	0.43	0.14	0.03	0
de02	0.09	0.17	0.36	0.26	0.10	0.02	0
de03	0.10	0.17	0.35	0.27	0.09	0.03	0
de04	0.07	0.26	0.45	0.14	0.05	0.02	0
de05	0.02	0.03	0.10	0.28	0.34	0.23	0
de06	0.10	0.17	0.32	0.28	0.11	0.03	0
de07	0.02	0.06	0.27	0.42	0.20	0.03	0
de08	0.04	0.10	0.24	0.44	0.15	0.03	0
de09	0.01	0.06	0.13	0.27	0.33	0.20	0
de10	0.10	0.15	0.30	0.34	0.10	0.02	0
de11	0.07	0.20	0.28	0.31	0.12	0.03	0

Understanding

un1 <- psych::alpha(
  taia %>% select(all_of(un_items)),
  cumulative = TRUE,
  title = "Understanding Factor",
  check.keys = FALSE
)

kable(un1$total,
      caption = "Understanding. Subscale statistics", 
      label = 27, digits = 2,
      col.names = total_colnames)

Table 27: Understanding. Subscale statistics

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Scale Mean	Total Score SD	Median interitem correlation
	0.92	0.92	0.92	0.5	12	0.01	31.24	10.15	0.51

un1$item.stats$mean <- un1$item.stats$mean / 5
kable(un1$item.stats,
      caption = "Understanding. Items statistics",
      label = 28, digits = 2,
      col.names = item_stats_colnames)

Table 28: Understanding. Items statistics

	Num. of Obs.	Discrimination	Std Cor	Cor Overlap Corrected	Cor if drop	Difficulty	SD
un01	495	0.75	0.75	0.73	0.70	0.59	1.05
un02	495	0.84	0.84	0.84	0.81	0.49	1.14
un03	495	0.59	0.59	0.54	0.51	0.60	1.17
un04	495	0.76	0.76	0.73	0.71	0.52	1.09
un05	495	0.81	0.81	0.80	0.77	0.56	1.10
un06	495	0.57	0.56	0.50	0.48	0.46	1.23
un07	495	0.72	0.72	0.69	0.66	0.43	1.18
un08	495	0.76	0.76	0.75	0.71	0.58	1.16
un09	495	0.73	0.73	0.69	0.67	0.46	1.23
un10	495	0.75	0.75	0.72	0.69	0.45	1.15
un11	495	0.79	0.79	0.77	0.74	0.53	1.20
un12	495	0.75	0.76	0.73	0.70	0.58	1.12

un1$item.stats %>%
  ggplot(aes(x = row.names(un1$item.stats))) +
  geom_point(aes(y = mean), color = "darkblue", size = 3) +
  geom_point(aes(y = raw.r), color = "darkred", size = 2) +
  geom_hline(yintercept = 0.1, color = "darkblue") +
  geom_hline(yintercept = 0.9, color = "darkblue") +
  geom_hline(yintercept = 0.25, color = "darkred") +
  geom_hline(yintercept = 0, color = "black") +
  labs(x = "Item", y = "Value",
       title = "Understanding. Items characteristics",
       subtitle = "Difficulty (blue) and Dicrimination (red)") +
  theme(plot.title = element_text(hjust = .5),
        plot.subtitle = element_text(hjust = .5))

kable(un1$alpha.drop,
      caption = "Understanding. Subscale statistics when item drop",
      label = 29, digits = 2,
      col.names = alpha_drop_colnames)

Table 29: Understanding. Subscale statistics when item drop

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Var(r)	Median interitem correlation
un01	0.91	0.92	0.91	0.50	10.87	0.01	0.01	0.51
un02	0.91	0.91	0.91	0.48	10.26	0.01	0.01	0.50
un03	0.92	0.92	0.92	0.52	12.05	0.01	0.01	0.54
un04	0.91	0.92	0.92	0.50	10.82	0.01	0.01	0.51
un05	0.91	0.91	0.91	0.49	10.46	0.01	0.01	0.50
un06	0.92	0.92	0.92	0.53	12.30	0.01	0.01	0.54
un07	0.92	0.92	0.92	0.50	11.10	0.01	0.01	0.51
un08	0.91	0.92	0.91	0.50	10.80	0.01	0.01	0.51
un09	0.92	0.92	0.92	0.50	11.06	0.01	0.01	0.51
un10	0.91	0.92	0.92	0.50	10.93	0.01	0.01	0.51
un11	0.91	0.91	0.91	0.49	10.62	0.01	0.01	0.50
un12	0.91	0.92	0.92	0.50	10.86	0.01	0.01	0.50

kable(un1$response.freq,
      caption = "Understanding. Non missing response frequency for each item",
      label = 30, digits = 2)

Table 30: Understanding. Non missing response frequency for each item

	0	1	2	3	4	5	miss
un01	0.02	0.07	0.19	0.43	0.24	0.05	0
un02	0.05	0.14	0.29	0.35	0.14	0.03	0
un03	0.03	0.08	0.16	0.36	0.29	0.07	0
un04	0.03	0.13	0.24	0.40	0.17	0.02	0
un05	0.04	0.08	0.19	0.44	0.21	0.04	0
un06	0.06	0.24	0.28	0.25	0.14	0.04	0
un07	0.09	0.21	0.30	0.29	0.09	0.02	0
un08	0.04	0.09	0.18	0.39	0.23	0.06	0
un09	0.08	0.18	0.25	0.30	0.17	0.01	0
un10	0.06	0.20	0.33	0.27	0.12	0.02	0
un11	0.05	0.13	0.23	0.36	0.18	0.05	0
un12	0.03	0.08	0.19	0.41	0.23	0.06	0

omega(taia %>% ungroup() %>% select(all_of(taia_items)),
      nfactors=6, p=.05, poly=FALSE,
      digits=2, title="Omega", sl=TRUE, plot=TRUE, covar=FALSE)

Omega 
Call: omegah(m = m, nfactors = nfactors, fm = fm, key = key, flip = flip, 
    digits = digits, title = title, sl = sl, labels = labels, 
    plot = plot, n.obs = n.obs, rotate = rotate, Phi = Phi, option = option, 
    covar = covar)
Alpha:                 0.94 
G.6:                   0.97 
Omega Hierarchical:    0.6 
Omega H asymptotic:    0.62 
Omega Total            0.96 

Schmid Leiman Factor loadings greater than  0.2 
          g   F1*   F2*   F3*   F4*   F5*   F6*   h2   u2   p2
pr01   0.57  0.34        0.26                   0.57 0.43 0.58
pr02   0.45                                     0.32 0.68 0.65
pr03   0.20                                0.54 0.39 0.61 0.10
pr04                                       0.43 0.24 0.76 0.02
pr05   0.56                          0.45       0.52 0.48 0.60
pr06   0.43  0.37                               0.35 0.65 0.53
pr07   0.57  0.24        0.25        0.21       0.50 0.50 0.66
pr08   0.52  0.38        0.23                   0.49 0.51 0.54
pr09   0.41  0.29                               0.29 0.71 0.57
pr10   0.37  0.25                               0.23 0.77 0.58
co01   0.51              0.51                   0.54 0.46 0.48
co02   0.44              0.55                   0.49 0.51 0.39
co03   0.47  0.29                               0.37 0.63 0.60
co04   0.33  0.44                               0.38 0.62 0.28
co05   0.44              0.63                   0.60 0.40 0.33
co06   0.37              0.51                   0.40 0.60 0.34
co07-        0.29                               0.17 0.83 0.11
co08                     0.34             -0.37 0.41 0.59 0.02
co09   0.40              0.60                   0.54 0.46 0.29
co10   0.38              0.45                   0.40 0.60 0.36
ut01   0.36  0.67                               0.61 0.39 0.21
ut02   0.45  0.63                               0.64 0.36 0.31
ut03   0.22  0.32                          0.52 0.54 0.46 0.09
ut04   0.27  0.39                               0.24 0.76 0.31
ut05   0.41  0.44                               0.37 0.63 0.45
ut06   0.46  0.60                               0.56 0.44 0.38
ut07   0.34  0.46                               0.34 0.66 0.35
ut08   0.40  0.47                               0.40 0.60 0.39
ut09   0.42  0.46                               0.39 0.61 0.44
ut10                                       0.24 0.09 0.91 0.03
ut11   0.54  0.21                    0.39       0.48 0.52 0.61
ut12   0.46  0.47                               0.45 0.55 0.47
fa01   0.44                    0.61             0.60 0.40 0.33
fa02                           0.67             0.54 0.46 0.00
fa03                                      -0.37 0.31 0.69 0.12
fa04   0.35              0.32        0.21       0.40 0.60 0.32
fa05   0.47                    0.60             0.62 0.38 0.36
fa06   0.58              0.30                   0.52 0.48 0.65
fa07   0.23                          0.20  0.47 0.36 0.64 0.14
fa08                           0.61             0.49 0.51 0.00
fa09                           0.64        0.23 0.55 0.45 0.02
fa10   0.24                    0.63             0.48 0.52 0.12
de01   0.43                                     0.29 0.71 0.63
de02   0.57              0.23        0.30       0.49 0.51 0.67
de03   0.50                          0.28       0.38 0.62 0.65
de04-  0.31  0.39                               0.27 0.73 0.37
de05   0.38  0.41                          0.29 0.45 0.55 0.32
de06   0.58                          0.47       0.58 0.42 0.59
de07   0.49  0.34                               0.40 0.60 0.59
de08   0.54  0.23                    0.25       0.43 0.57 0.68
de09   0.22                                0.59 0.43 0.57 0.12
de10   0.60                          0.40       0.56 0.44 0.64
de11   0.22                          0.24  0.32 0.27 0.73 0.18
un01   0.25        0.72                         0.63 0.37 0.10
un02   0.28        0.79                         0.70 0.30 0.11
un03               0.43       -0.26             0.36 0.64 0.10
un04   0.25        0.68                         0.53 0.47 0.12
un05   0.28        0.77                         0.67 0.33 0.11
un06        -0.29  0.51                    0.32 0.40 0.60 0.02
un07   0.33        0.59                         0.54 0.46 0.20
un08   0.24        0.73                         0.60 0.40 0.10
un09   0.31        0.61                         0.52 0.48 0.18
un10   0.27        0.65                         0.57 0.43 0.13
un11   0.24        0.72                         0.60 0.40 0.10
un12   0.26        0.68                         0.57 0.43 0.12

With eigenvalues of:
  g F1* F2* F3* F4* F5* F6* 
9.4 4.6 5.6 2.8 2.7 1.6 2.3 

general/max  1.68   max/min =   3.6
mean percent general =  0.32    with sd =  0.22 and cv of  0.68 
Explained Common Variance of the general factor =  0.32 

The degrees of freedom are 1705  and the fit is  8.03 
The number of observations was  495  with Chi Square =  3753.55  with prob <  2.4e-155
The root mean square of the residuals is  0.04 
The df corrected root mean square of the residuals is  0.04
RMSEA index =  0.049  and the 10 % confidence intervals are  0.047 0.051
BIC =  -6825.22

Compare this with the adequacy of just a general factor and no group factors
The degrees of freedom for just the general factor are 2015  and the fit is  22.88 
The number of observations was  495  with Chi Square =  10774.78  with prob <  0
The root mean square of the residuals is  0.15 
The df corrected root mean square of the residuals is  0.15 

RMSEA index =  0.094  and the 10 % confidence intervals are  0.092 0.096
BIC =  -1727.41 

Measures of factor score adequacy             
                                                 g  F1*  F2*  F3*
Correlation of scores with factors            0.81 0.89 0.97 0.86
Multiple R square of scores with factors      0.66 0.79 0.94 0.74
Minimum correlation of factor score estimates 0.32 0.59 0.88 0.47
                                               F4*  F5*  F6*
Correlation of scores with factors            0.94 0.71 0.91
Multiple R square of scores with factors      0.88 0.50 0.83
Minimum correlation of factor score estimates 0.76 0.00 0.66

 Total, General and Subset omega for each subset
                                                 g  F1*  F2*  F3*
Omega total for total scores and subscales    0.96 0.87 0.91 0.86
Omega general for total scores and subscales  0.60 0.43 0.11 0.45
Omega group for total scores and subscales    0.21 0.44 0.79 0.41
                                               F4*  F5*  F6*
Omega total for total scores and subscales    0.83 0.81 0.51
Omega general for total scores and subscales  0.09 0.57 0.14
Omega group for total scores and subscales    0.74 0.24 0.37

splitHalf(taia %>% ungroup() %>% select(all_of(taia_items)),
          raw=F, brute=F, n.sample=100, covar=F,
          check.keys=F, key=NULL, use="pairwise")

Split half reliabilities  
Call: splitHalf(r = taia %>% ungroup() %>% select(all_of(taia_items)), 
    raw = F, brute = F, n.sample = 100, covar = F, check.keys = F, 
    key = NULL, use = "pairwise")

Maximum split half reliability (lambda 4) =  0.96
Guttman lambda 6                          =  0.96
Average split half reliability            =  0.93
Guttman lambda 3 (alpha)                  =  0.93
Guttman lambda 2                          =  0.94
Minimum split half reliability  (beta)    =  0.88
Average interitem r =  0.17  with median =  0.18

guttman(taia %>% ungroup() %>% select(all_of(taia_items)))

Call: guttman(r = taia %>% ungroup() %>% select(all_of(taia_items)))

Alternative estimates of reliability

Guttman bounds 
L1 =  0.92 
L2 =  0.94 
L3 (alpha) =  0.93 
L4 (max) =  0.97 
L5 =  0.92 
L6 (smc) =  0.96 
TenBerge bounds 
mu0 =  0.93 mu1 =  0.94 mu2 =  0.94 mu3 =  0.94 

alpha of first PC =  0.95 
estimated greatest lower bound based upon communalities=  0.97 

beta found by splitHalf  =  0.84 

glb.fa(taia %>% ungroup() %>% select(all_of(taia_items)))

$glb
[1] 0.965817

$communality
     pr01      pr02      pr03      pr04      pr05      pr06      pr07 
0.7253391 0.5393523 0.4690491 0.6292470 0.7830601 0.6280428 0.5758103 
     pr08      pr09      pr10      co01      co02      co03      co04 
0.6112839 0.5896570 0.3330770 0.5758243 0.6305638 0.4895706 0.4890165 
     co05      co06      co07      co08      co09      co10      ut01 
0.7521395 0.5726406 0.4356987 0.4665793 0.6337356 0.4811587 0.7718201 
     ut02      ut03      ut04      ut05      ut06      ut07      ut08 
0.7277348 0.6422830 0.3722353 0.5234489 0.7171434 0.5757501 0.5792722 
     ut09      ut10      ut11      ut12      fa01      fa02      fa03 
0.7253062 0.3644927 0.6451266 0.5389414 0.6943597 0.5928412 0.4376811 
     fa04      fa05      fa06      fa07      fa08      fa09      fa10 
0.5197275 0.7565165 0.5844505 0.4786126 0.6061162 0.6945327 0.4919291 
     de01      de02      de03      de04      de05      de06      de07 
0.4216417 0.5711187 0.5654506 0.4521109 0.7942688 0.7264322 0.5278337 
     de08      de09      de10      de11      un01      un02      un03 
0.5885239 0.6875419 0.6514868 0.3425354 0.6718202 0.7379031 0.4402195 
     un04      un05      un06      un07      un08      un09      un10 
0.6398019 0.6914535 0.4729219 0.5759967 0.6904648 0.5762576 0.6507091 
     un11      un12 
0.6870705 0.6276157 

$numf
[1] 19

$Call
glb.fa(r = taia %>% ungroup() %>% select(all_of(taia_items)))

Items exclusion

First step

Excluded items: co07, ut10, de04

Reason: negative discrimination

co_items_old <- co_items
co_items[-7] -> co_items

ut_items_old <- ut_items
ut_items[-10] -> ut_items

de_items_old <- de_items
de_items[-4] -> de_items

Subscales after first step of exclusion

Consistency

co2 <- psych::alpha(
  taia %>% select(all_of(co_items)),
  cumulative = TRUE,
  title = "Consistency Factor",
  check.keys = FALSE
)

kable(co2$total,
      caption = "Consistency. Subscale statistics", 
      label = 11, digits = 2,
      col.names = total_colnames)

Table 11: Consistency. Subscale statistics

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Scale Mean	Total Score SD	Median interitem correlation
	0.83	0.82	0.83	0.34	4.7	0.01	22.44	6.24	0.36

co2$item.stats$mean <- co2$item.stats$mean / 5
kable(co2$item.stats,
      caption = "Consistency. Items statistics",
      label = 12, digits = 2,
      col.names = item_stats_colnames)

Table 12: Consistency. Items statistics

	Num. of Obs.	Discrimination	Std Cor	Cor Overlap Corrected	Cor if drop	Difficulty	SD
co01	495	0.74	0.74	0.71	0.65	0.50	1.08
co02	495	0.72	0.72	0.67	0.62	0.50	1.04
co03	495	0.56	0.57	0.48	0.43	0.57	1.02
co04	495	0.44	0.43	0.33	0.28	0.69	1.09
co05	495	0.79	0.78	0.78	0.70	0.44	1.11
co06	495	0.68	0.67	0.62	0.56	0.50	1.11
co08	495	0.44	0.44	0.34	0.29	0.38	1.04
co09	495	0.76	0.76	0.75	0.67	0.41	1.07
co10	495	0.68	0.68	0.62	0.57	0.49	1.10

co2$item.stats %>%
  ggplot(aes(x = row.names(co2$item.stats))) +
  geom_point(aes(y = mean), color = "darkblue", size = 3) +
  geom_point(aes(y = raw.r), color = "darkred", size = 2) +
  geom_hline(yintercept = 0.1, color = "darkblue") +
  geom_hline(yintercept = 0.9, color = "darkblue") +
  geom_hline(yintercept = 0.25, color = "darkred") +
  geom_hline(yintercept = 0, color = "black") +
  labs(x = "Item", y = "Value",
       title = "Consistency. Items characteristics",
       subtitle = "Difficulty (blue) and Dicrimination (red)") +
  theme(plot.title = element_text(hjust = .5),
        plot.subtitle = element_text(hjust = .5))

kable(co2$alpha.drop,
      caption = "Consistency. Subscale statistics when item drop",
      label = 13, digits = 2,
      col.names = alpha_drop_colnames)

Table 13: Consistency. Subscale statistics when item drop

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Var(r)	Median interitem correlation
co01	0.79	0.79	0.80	0.32	3.81	0.01	0.03	0.34
co02	0.80	0.80	0.81	0.33	3.89	0.01	0.03	0.35
co03	0.82	0.82	0.82	0.36	4.49	0.01	0.03	0.41
co04	0.84	0.83	0.83	0.39	5.04	0.01	0.02	0.41
co05	0.79	0.79	0.79	0.31	3.66	0.01	0.02	0.33
co06	0.80	0.80	0.81	0.34	4.06	0.01	0.03	0.35
co08	0.83	0.83	0.83	0.39	5.01	0.01	0.02	0.40
co09	0.79	0.79	0.80	0.32	3.74	0.01	0.02	0.34
co10	0.80	0.80	0.81	0.34	4.04	0.01	0.03	0.35

kable(co2$response.freq,
      caption = "Consistency. Non missing response frequency for each item",
      label = 14, digits = 2)

Table 14: Consistency. Non missing response frequency for each item

	0	1	2	3	4	5	miss
co01	0.05	0.11	0.31	0.39	0.11	0.03	0
co02	0.03	0.12	0.32	0.38	0.13	0.02	0
co03	0.02	0.07	0.22	0.44	0.21	0.04	0
co04	0.01	0.04	0.10	0.35	0.32	0.18	0
co05	0.06	0.19	0.37	0.27	0.09	0.02	0
co06	0.04	0.14	0.28	0.38	0.13	0.03	0
co08	0.08	0.27	0.42	0.16	0.06	0.01	0
co09	0.06	0.24	0.40	0.22	0.06	0.02	0
co10	0.04	0.14	0.33	0.34	0.11	0.03	0

Utility

ut2 <- psych::alpha(
  taia %>% select(all_of(ut_items)),
  cumulative = TRUE,
  title = "Utility Factor",
  check.keys = FALSE
)

kable(ut2$total,
      caption = "Utility. Subscale statistics", 
      label = 15, digits = 2,
      col.names = total_colnames)

Table 15: Utility. Subscale statistics

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Scale Mean	Total Score SD	Median interitem correlation
	0.88	0.88	0.88	0.4	7.4	0.01	35.92	8.32	0.41

ut2$item.stats$mean <- ut2$item.stats$mean / 5
kable(ut2$item.stats,
      caption = "Utility. Items statistics",
      label = 16, digits = 2,
      col.names = item_stats_colnames)

Table 16: Utility. Items statistics

	Num. of Obs.	Discrimination	Std Cor	Cor Overlap Corrected	Cor if drop	Difficulty	SD
ut01	495	0.79	0.79	0.79	0.73	0.76	1.05
ut02	495	0.83	0.84	0.84	0.79	0.70	1.05
ut03	495	0.55	0.56	0.49	0.45	0.71	1.11
ut04	495	0.53	0.53	0.46	0.42	0.62	1.11
ut05	495	0.69	0.68	0.64	0.60	0.61	1.21
ut06	495	0.77	0.77	0.75	0.71	0.65	1.10
ut07	495	0.62	0.62	0.57	0.52	0.64	1.13
ut08	495	0.66	0.67	0.62	0.58	0.69	1.05
ut09	495	0.70	0.70	0.66	0.62	0.64	1.17
ut11	495	0.57	0.56	0.49	0.46	0.53	1.23
ut12	495	0.72	0.72	0.68	0.65	0.63	1.15

ut2$item.stats %>%
  ggplot(aes(x = row.names(ut2$item.stats))) +
  geom_point(aes(y = mean), color = "darkblue", size = 3) +
  geom_point(aes(y = raw.r), color = "darkred", size = 2) +
  geom_hline(yintercept = 0.1, color = "darkblue") +
  geom_hline(yintercept = 0.9, color = "darkblue") +
  geom_hline(yintercept = 0.25, color = "darkred") +
  geom_hline(yintercept = 0, color = "black") +
  labs(x = "Item", y = "Value",
       title = "Utility. Items characteristics",
       subtitle = "Difficulty (blue) and Dicrimination (red)") +
  theme(plot.title = element_text(hjust = .5),
        plot.subtitle = element_text(hjust = .5))

kable(ut2$alpha.drop,
      caption = "Utility. Subscale statistics when item drop",
      label = 17, digits = 2,
      col.names = alpha_drop_colnames)

Table 17: Utility. Subscale statistics when item drop

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Var(r)	Median interitem correlation
ut01	0.86	0.86	0.86	0.38	6.21	0.01	0.01	0.40
ut02	0.86	0.86	0.86	0.38	6.01	0.01	0.01	0.37
ut03	0.88	0.88	0.88	0.42	7.30	0.01	0.01	0.43
ut04	0.88	0.88	0.88	0.43	7.41	0.01	0.01	0.43
ut05	0.87	0.87	0.87	0.40	6.69	0.01	0.01	0.41
ut06	0.86	0.86	0.87	0.39	6.30	0.01	0.01	0.41
ut07	0.87	0.87	0.87	0.41	6.99	0.01	0.01	0.42
ut08	0.87	0.87	0.87	0.40	6.77	0.01	0.01	0.41
ut09	0.87	0.87	0.87	0.40	6.64	0.01	0.02	0.41
ut11	0.88	0.88	0.88	0.42	7.27	0.01	0.01	0.44
ut12	0.86	0.87	0.87	0.39	6.52	0.01	0.02	0.41

kable(ut2$response.freq,
      caption = "Utility. Non missing response frequency for each item",
      label = 18, digits = 2)

Table 18: Utility. Non missing response frequency for each item

	0	1	2	3	4	5	miss
ut01	0.01	0.01	0.06	0.29	0.34	0.28	0
ut02	0.01	0.02	0.09	0.38	0.30	0.20	0
ut03	0.01	0.04	0.09	0.33	0.31	0.22	0
ut04	0.02	0.08	0.15	0.40	0.27	0.09	0
ut05	0.03	0.06	0.20	0.35	0.23	0.12	0
ut06	0.03	0.03	0.13	0.39	0.30	0.12	0
ut07	0.01	0.05	0.19	0.35	0.26	0.14	0
ut08	0.01	0.03	0.11	0.36	0.34	0.15	0
ut09	0.03	0.05	0.15	0.38	0.25	0.13	0
ut11	0.05	0.12	0.27	0.32	0.18	0.07	0
ut12	0.02	0.07	0.15	0.38	0.26	0.12	0

Dependability

de2 <- psych::alpha(
  taia %>% select(all_of(de_items)),
  cumulative = TRUE,
  title = "Dependability Factor",
  check.keys = FALSE
)

kable(de2$total,
      caption = "Dependability. Subscale statistics", 
      label = 23, digits = 2,
      col.names = total_colnames)

Table 23: Dependability. Subscale statistics

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Scale Mean	Total Score SD	Median interitem correlation
	0.82	0.82	0.84	0.31	4.49	0.01	26.19	7.05	0.32

de2$item.stats$mean <- de2$item.stats$mean / 5
kable(de2$item.stats,
      caption = "Dependability. Items statistics",
      label = 24, digits = 2,
      col.names = item_stats_colnames)

Table 24: Dependability. Items statistics

	Num. of Obs.	Discrimination	Std Cor	Cor Overlap Corrected	Cor if drop	Difficulty	SD
de01	495	0.58	0.59	0.53	0.47	0.52	1.10
de02	495	0.72	0.72	0.68	0.62	0.43	1.15
de03	495	0.65	0.65	0.60	0.54	0.43	1.19
de05	495	0.62	0.62	0.59	0.50	0.71	1.16
de06	495	0.67	0.67	0.62	0.56	0.45	1.23
de07	495	0.61	0.62	0.56	0.51	0.56	1.00
de08	495	0.70	0.71	0.67	0.61	0.53	1.06
de09	495	0.46	0.45	0.40	0.31	0.69	1.20
de10	495	0.73	0.73	0.71	0.64	0.45	1.18
de11	495	0.41	0.40	0.28	0.25	0.46	1.20

de2$item.stats %>%
  ggplot(aes(x = row.names(de2$item.stats))) +
  geom_point(aes(y = mean), color = "darkblue", size = 3) +
  geom_point(aes(y = raw.r), color = "darkred", size = 2) +
  geom_hline(yintercept = 0.1, color = "darkblue") +
  geom_hline(yintercept = 0.9, color = "darkblue") +
  geom_hline(yintercept = 0.25, color = "darkred") +
  geom_hline(yintercept = 0, color = "black") +
  labs(x = "Item", y = "Value",
       title = "Dependability. Items characteristics",
       subtitle = "Difficulty (blue) and Dicrimination (red)") +
  theme(plot.title = element_text(hjust = .5),
        plot.subtitle = element_text(hjust = .5))

kable(de2$alpha.drop,
      caption = "Dependability. Subscale statistics when item drop",
      label = 25, digits = 2,
      col.names = alpha_drop_colnames)

Table 25: Dependability. Subscale statistics when item drop

	Alpha	Standardized Alpha	Guttman’s Lambda 6	Average interitem correlation	S/N	Alpha SE	Var(r)	Median interitem correlation
de01	0.80	0.80	0.82	0.31	4.11	0.01	0.02	0.31
de02	0.79	0.79	0.81	0.29	3.72	0.01	0.02	0.29
de03	0.79	0.80	0.82	0.30	3.93	0.01	0.02	0.29
de05	0.80	0.80	0.80	0.31	4.04	0.01	0.02	0.35
de06	0.79	0.80	0.81	0.30	3.88	0.01	0.02	0.31
de07	0.80	0.80	0.82	0.31	4.02	0.01	0.02	0.29
de08	0.79	0.79	0.81	0.29	3.75	0.01	0.02	0.29
de09	0.82	0.82	0.82	0.34	4.60	0.01	0.02	0.35
de10	0.78	0.79	0.80	0.29	3.67	0.01	0.02	0.29
de11	0.83	0.83	0.84	0.35	4.79	0.01	0.02	0.37

kable(de2$response.freq,
      caption = "Dependability. Non missing response frequency for each item",
      label = 26, digits = 2)

Table 26: Dependability. Non missing response frequency for each item

	0	1	2	3	4	5	miss
de01	0.05	0.11	0.24	0.43	0.14	0.03	0
de02	0.09	0.17	0.36	0.26	0.10	0.02	0
de03	0.10	0.17	0.35	0.27	0.09	0.03	0
de05	0.02	0.03	0.10	0.28	0.34	0.23	0
de06	0.10	0.17	0.32	0.28	0.11	0.03	0
de07	0.02	0.06	0.27	0.42	0.20	0.03	0
de08	0.04	0.10	0.24	0.44	0.15	0.03	0
de09	0.01	0.06	0.13	0.27	0.33	0.20	0
de10	0.10	0.15	0.30	0.34	0.10	0.02	0
de11	0.07	0.20	0.28	0.31	0.12	0.03	0

Reliability measures

omega(taia %>% ungroup() %>% select(all_of(taia_items)),
      nfactors=6, p=.05, poly=FALSE,
      digits=2, title="Omega", sl=TRUE, plot=TRUE, covar=FALSE)

Omega 
Call: omegah(m = m, nfactors = nfactors, fm = fm, key = key, flip = flip, 
    digits = digits, title = title, sl = sl, labels = labels, 
    plot = plot, n.obs = n.obs, rotate = rotate, Phi = Phi, option = option, 
    covar = covar)
Alpha:                 0.94 
G.6:                   0.97 
Omega Hierarchical:    0.6 
Omega H asymptotic:    0.62 
Omega Total            0.96 

Schmid Leiman Factor loadings greater than  0.2 
          g   F1*   F2*   F3*   F4*   F5*   F6*   h2   u2   p2
pr01   0.57  0.34        0.26                   0.57 0.43 0.58
pr02   0.45                                     0.32 0.68 0.65
pr03   0.20                                0.54 0.39 0.61 0.10
pr04                                       0.43 0.24 0.76 0.02
pr05   0.56                          0.45       0.52 0.48 0.60
pr06   0.43  0.37                               0.35 0.65 0.53
pr07   0.57  0.24        0.25        0.21       0.50 0.50 0.66
pr08   0.52  0.38        0.23                   0.49 0.51 0.54
pr09   0.41  0.29                               0.29 0.71 0.57
pr10   0.37  0.25                               0.23 0.77 0.58
co01   0.51              0.51                   0.54 0.46 0.48
co02   0.44              0.55                   0.49 0.51 0.39
co03   0.47  0.29                               0.37 0.63 0.60
co04   0.33  0.44                               0.38 0.62 0.28
co05   0.44              0.63                   0.60 0.40 0.33
co06   0.37              0.51                   0.40 0.60 0.34
co07-        0.29                               0.17 0.83 0.11
co08                     0.34             -0.37 0.41 0.59 0.02
co09   0.40              0.60                   0.54 0.46 0.29
co10   0.38              0.45                   0.40 0.60 0.36
ut01   0.36  0.67                               0.61 0.39 0.21
ut02   0.45  0.63                               0.64 0.36 0.31
ut03   0.22  0.32                          0.52 0.54 0.46 0.09
ut04   0.27  0.39                               0.24 0.76 0.31
ut05   0.41  0.44                               0.37 0.63 0.45
ut06   0.46  0.60                               0.56 0.44 0.38
ut07   0.34  0.46                               0.34 0.66 0.35
ut08   0.40  0.47                               0.40 0.60 0.39
ut09   0.42  0.46                               0.39 0.61 0.44
ut10                                       0.24 0.09 0.91 0.03
ut11   0.54  0.21                    0.39       0.48 0.52 0.61
ut12   0.46  0.47                               0.45 0.55 0.47
fa01   0.44                    0.61             0.60 0.40 0.33
fa02                           0.67             0.54 0.46 0.00
fa03                                      -0.37 0.31 0.69 0.12
fa04   0.35              0.32        0.21       0.40 0.60 0.32
fa05   0.47                    0.60             0.62 0.38 0.36
fa06   0.58              0.30                   0.52 0.48 0.65
fa07   0.23                          0.20  0.47 0.36 0.64 0.14
fa08                           0.61             0.49 0.51 0.00
fa09                           0.64        0.23 0.55 0.45 0.02
fa10   0.24                    0.63             0.48 0.52 0.12
de01   0.43                                     0.29 0.71 0.63
de02   0.57              0.23        0.30       0.49 0.51 0.67
de03   0.50                          0.28       0.38 0.62 0.65
de04-  0.31  0.39                               0.27 0.73 0.37
de05   0.38  0.41                          0.29 0.45 0.55 0.32
de06   0.58                          0.47       0.58 0.42 0.59
de07   0.49  0.34                               0.40 0.60 0.59
de08   0.54  0.23                    0.25       0.43 0.57 0.68
de09   0.22                                0.59 0.43 0.57 0.12
de10   0.60                          0.40       0.56 0.44 0.64
de11   0.22                          0.24  0.32 0.27 0.73 0.18
un01   0.25        0.72                         0.63 0.37 0.10
un02   0.28        0.79                         0.70 0.30 0.11
un03               0.43       -0.26             0.36 0.64 0.10
un04   0.25        0.68                         0.53 0.47 0.12
un05   0.28        0.77                         0.67 0.33 0.11
un06        -0.29  0.51                    0.32 0.40 0.60 0.02
un07   0.33        0.59                         0.54 0.46 0.20
un08   0.24        0.73                         0.60 0.40 0.10
un09   0.31        0.61                         0.52 0.48 0.18
un10   0.27        0.65                         0.57 0.43 0.13
un11   0.24        0.72                         0.60 0.40 0.10
un12   0.26        0.68                         0.57 0.43 0.12

With eigenvalues of:
  g F1* F2* F3* F4* F5* F6* 
9.4 4.6 5.6 2.8 2.7 1.6 2.3 

general/max  1.68   max/min =   3.6
mean percent general =  0.32    with sd =  0.22 and cv of  0.68 
Explained Common Variance of the general factor =  0.32 

The degrees of freedom are 1705  and the fit is  8.03 
The number of observations was  495  with Chi Square =  3753.55  with prob <  2.4e-155
The root mean square of the residuals is  0.04 
The df corrected root mean square of the residuals is  0.04
RMSEA index =  0.049  and the 10 % confidence intervals are  0.047 0.051
BIC =  -6825.22

Compare this with the adequacy of just a general factor and no group factors
The degrees of freedom for just the general factor are 2015  and the fit is  22.88 
The number of observations was  495  with Chi Square =  10774.78  with prob <  0
The root mean square of the residuals is  0.15 
The df corrected root mean square of the residuals is  0.15 

RMSEA index =  0.094  and the 10 % confidence intervals are  0.092 0.096
BIC =  -1727.41 

Measures of factor score adequacy             
                                                 g  F1*  F2*  F3*
Correlation of scores with factors            0.81 0.89 0.97 0.86
Multiple R square of scores with factors      0.66 0.79 0.94 0.74
Minimum correlation of factor score estimates 0.32 0.59 0.88 0.47
                                               F4*  F5*  F6*
Correlation of scores with factors            0.94 0.71 0.91
Multiple R square of scores with factors      0.88 0.50 0.83
Minimum correlation of factor score estimates 0.76 0.00 0.66

 Total, General and Subset omega for each subset
                                                 g  F1*  F2*  F3*
Omega total for total scores and subscales    0.96 0.87 0.91 0.86
Omega general for total scores and subscales  0.60 0.43 0.11 0.45
Omega group for total scores and subscales    0.21 0.44 0.79 0.41
                                               F4*  F5*  F6*
Omega total for total scores and subscales    0.83 0.81 0.51
Omega general for total scores and subscales  0.09 0.57 0.14
Omega group for total scores and subscales    0.74 0.24 0.37

splitHalf(taia %>% ungroup() %>% select(all_of(taia_items)),
          raw=F, brute=F, n.sample=100, covar=F,
          check.keys=F, key=NULL, use="pairwise")

Split half reliabilities  
Call: splitHalf(r = taia %>% ungroup() %>% select(all_of(taia_items)), 
    raw = F, brute = F, n.sample = 100, covar = F, check.keys = F, 
    key = NULL, use = "pairwise")

Maximum split half reliability (lambda 4) =  0.96
Guttman lambda 6                          =  0.96
Average split half reliability            =  0.93
Guttman lambda 3 (alpha)                  =  0.93
Guttman lambda 2                          =  0.94
Minimum split half reliability  (beta)    =  0.87
Average interitem r =  0.17  with median =  0.18

guttman(taia %>% ungroup() %>% select(all_of(taia_items)))

Call: guttman(r = taia %>% ungroup() %>% select(all_of(taia_items)))

Alternative estimates of reliability

Guttman bounds 
L1 =  0.92 
L2 =  0.94 
L3 (alpha) =  0.93 
L4 (max) =  0.97 
L5 =  0.92 
L6 (smc) =  0.96 
TenBerge bounds 
mu0 =  0.93 mu1 =  0.94 mu2 =  0.94 mu3 =  0.94 

alpha of first PC =  0.95 
estimated greatest lower bound based upon communalities=  0.97 

beta found by splitHalf  =  0.85 

glb.fa(taia %>% ungroup() %>% select(all_of(taia_items)))

$glb
[1] 0.965817

$communality
     pr01      pr02      pr03      pr04      pr05      pr06      pr07 
0.7253391 0.5393523 0.4690491 0.6292470 0.7830601 0.6280428 0.5758103 
     pr08      pr09      pr10      co01      co02      co03      co04 
0.6112839 0.5896570 0.3330770 0.5758243 0.6305638 0.4895706 0.4890165 
     co05      co06      co07      co08      co09      co10      ut01 
0.7521395 0.5726406 0.4356987 0.4665793 0.6337356 0.4811587 0.7718201 
     ut02      ut03      ut04      ut05      ut06      ut07      ut08 
0.7277348 0.6422830 0.3722353 0.5234489 0.7171434 0.5757501 0.5792722 
     ut09      ut10      ut11      ut12      fa01      fa02      fa03 
0.7253062 0.3644927 0.6451266 0.5389414 0.6943597 0.5928412 0.4376811 
     fa04      fa05      fa06      fa07      fa08      fa09      fa10 
0.5197275 0.7565165 0.5844505 0.4786126 0.6061162 0.6945327 0.4919291 
     de01      de02      de03      de04      de05      de06      de07 
0.4216417 0.5711187 0.5654506 0.4521109 0.7942688 0.7264322 0.5278337 
     de08      de09      de10      de11      un01      un02      un03 
0.5885239 0.6875419 0.6514868 0.3425354 0.6718202 0.7379031 0.4402195 
     un04      un05      un06      un07      un08      un09      un10 
0.6398019 0.6914535 0.4729219 0.5759967 0.6904648 0.5762576 0.6507091 
     un11      un12 
0.6870705 0.6276157 

$numf
[1] 19

$Call
glb.fa(r = taia %>% ungroup() %>% select(all_of(taia_items)))

Exploratory Factor Analysis

taia_items <- c(
  pr_items, co_items, ut_items, fa_items, de_items, un_items
)

6 factors, varimax rotation

efa_6f_vm <- factanal(taia %>% select(all_of(taia_items)),
                   factors = 6,
                   scores = "regression",
                   rotation = "varimax")

loadings(efa_6f_vm)

Loadings:
     Factor1 Factor2 Factor3 Factor4 Factor5 Factor6
pr01  0.489   0.475   0.172           0.287         
pr02  0.263   0.392   0.219           0.164   0.181 
pr03  0.219                           0.547         
pr04         -0.109           0.139   0.437         
pr05  0.204   0.350   0.139           0.123   0.676 
pr06  0.475   0.279   0.144                   0.105 
pr07  0.387   0.525                   0.208   0.134 
pr08  0.492   0.429   0.125           0.241         
pr09  0.350   0.347   0.133           0.220         
pr10  0.328   0.301   0.124           0.108         
co01  0.243   0.676           0.116                 
co02  0.169   0.626   0.115                         
co03  0.416   0.370                   0.159   0.141 
co04  0.532   0.147   0.121           0.161         
co05  0.137   0.724                                 
co06  0.152   0.554          -0.117                 
co08 -0.118   0.413  -0.115  -0.127  -0.467         
co09          0.676                  -0.160         
co10  0.184   0.526   0.206          -0.123         
ut01  0.810                                         
ut02  0.806           0.102           0.135   0.125 
ut03  0.472  -0.102           0.119   0.507         
ut04  0.461                   0.104           0.132 
ut05  0.598   0.194                                 
ut06  0.717   0.164                           0.125 
ut07  0.550   0.207                                 
ut08  0.576   0.249                                 
ut09  0.593   0.174                   0.102   0.128 
ut11  0.368   0.255   0.158           0.126   0.591 
ut12  0.604   0.233   0.135           0.142         
fa01  0.300   0.345           0.628                 
fa02                 -0.207   0.669   0.148         
fa03 -0.116   0.385                  -0.318   0.148 
fa04          0.549           0.103  -0.192   0.177 
fa05  0.293   0.411           0.622                 
fa06  0.301   0.573   0.126   0.188   0.182   0.163 
fa07                          0.196   0.474   0.193 
fa08                 -0.191   0.602   0.232         
fa09                 -0.155   0.631   0.310         
fa10  0.280   0.136           0.599                 
de01  0.278   0.429   0.162                         
de02  0.225   0.571   0.129           0.155   0.228 
de03  0.223   0.475   0.115   0.138           0.214 
de05  0.508   0.173   0.137           0.385         
de06  0.218   0.352   0.184   0.171           0.666 
de07  0.439   0.301   0.220                   0.182 
de08  0.345   0.412   0.193   0.107   0.185   0.205 
de09  0.259                           0.592         
de10  0.287   0.512           0.177           0.351 
de11                          0.181   0.332   0.255 
un01  0.287           0.731                         
un02          0.138   0.815                         
un03  0.207           0.502  -0.247                 
un04          0.113   0.711                         
un05  0.191           0.791                         
un06 -0.131           0.518           0.189         
un07          0.286   0.648          -0.139   0.128 
un08  0.182           0.746                         
un09          0.162   0.662                   0.197 
un10          0.261   0.690                         
un11                  0.763                         
un12  0.236           0.713                         

               Factor1 Factor2 Factor3 Factor4 Factor5 Factor6
SS loadings      7.605   7.077   6.534   2.832   2.786   2.029
Proportion Var   0.123   0.114   0.105   0.046   0.045   0.033
Cumulative Var   0.123   0.237   0.342   0.388   0.433   0.466

kable(sort(efa_6f_vm$uniquenesses, decreasing = TRUE), col.names = "U")

	U
de11	0.7817421
pr04	0.7700534
pr10	0.7616189
ut04	0.7559106
fa03	0.7134353
de01	0.7002496
fa07	0.6907293
pr09	0.6888357
un06	0.6751271
pr02	0.6694849
pr06	0.6576002
ut07	0.6510578
co04	0.6481729
co06	0.6474121
de03	0.6464066
un03	0.6402866
pr03	0.6384384
co03	0.6327467
co10	0.6282188
de07	0.6246089
fa04	0.6137315
ut08	0.5910384
ut05	0.5868681
ut09	0.5865585
de08	0.5858475
de09	0.5766570
co08	0.5671255
co02	0.5579891
de05	0.5437340
fa10	0.5420869
ut12	0.5382611
fa08	0.5284220
de02	0.5246474
co09	0.5063667
pr07	0.4996945
pr08	0.4983024
ut03	0.4937529
de10	0.4934491
un09	0.4875879
fa09	0.4737183
fa02	0.4731288
fa06	0.4702934
un04	0.4642368
co01	0.4635405
un07	0.4574466
co05	0.4479825
ut06	0.4362455
un10	0.4358851
un12	0.4312571
pr01	0.4144342
ut11	0.4071750
un08	0.4066783
un11	0.3931924
fa01	0.3816574
un01	0.3730108
fa05	0.3486393
pr05	0.3357658
ut01	0.3321338
un05	0.3254634
de06	0.3122163
un02	0.3085120
ut02	0.3006345

6 factors, promax rotation

efa_6f_pm <- factanal(taia %>% select(all_of(taia_items)),
                   factors = 6,
                   scores = "regression",
                   rotation = "promax")

loadings(efa_6f_pm)

Loadings:
     Factor1 Factor2 Factor3 Factor4 Factor5 Factor6
pr01  0.461           0.225   0.283                 
pr02  0.338   0.110           0.148           0.136 
pr03         -0.110           0.614                 
pr04 -0.141                   0.484                 
pr05                                          0.790 
pr06  0.174           0.410                         
pr07  0.527           0.131   0.192                 
pr08  0.422           0.278   0.238                 
pr09  0.361           0.146   0.227                 
pr10  0.263           0.204          -0.122         
co01  0.809                           0.102  -0.145 
co02  0.765                                  -0.137 
co03  0.303           0.264   0.114                 
co04                  0.493   0.121          -0.132 
co05  0.902  -0.102  -0.117                  -0.109 
co06  0.668                          -0.154         
co08  0.542  -0.180          -0.501  -0.100         
co09  0.817  -0.113  -0.123  -0.169                 
co10  0.598   0.115          -0.135                 
ut01 -0.249           0.974                         
ut02 -0.231           0.910                   0.113 
ut03 -0.213           0.385   0.515                 
ut04 -0.198           0.552                   0.146 
ut05                  0.658  -0.124                 
ut06                  0.789                   0.108 
ut07  0.128           0.593                         
ut08  0.186           0.543                  -0.108 
ut09                  0.608                   0.110 
ut11                  0.291                   0.694 
ut12  0.106           0.559                         
fa01  0.277   0.125   0.171           0.650         
fa02                 -0.129           0.695         
fa03  0.418          -0.154  -0.379           0.158 
fa04  0.609          -0.225  -0.241           0.146 
fa05  0.367   0.105   0.156  -0.119   0.648         
fa06  0.580                   0.149   0.131         
fa07                 -0.218   0.508   0.109   0.173 
fa08                 -0.179   0.165   0.604         
fa09                 -0.187   0.254   0.627         
fa10                  0.281  -0.127   0.648  -0.119 
de01  0.460                                         
de02  0.569                   0.135           0.166 
de03  0.430                                   0.173 
de05  0.114           0.340   0.407  -0.107         
de06                                          0.770 
de07  0.160   0.109   0.337                   0.156 
de08  0.329           0.129   0.141           0.153 
de09                          0.692  -0.101         
de10  0.397           0.106           0.103   0.339 
de11         -0.106  -0.103   0.320   0.101   0.273 
un01 -0.148   0.804   0.225           0.123  -0.141 
un02          0.857  -0.105                         
un03          0.451   0.145          -0.247         
un04          0.734                                 
un05          0.844                                 
un06          0.556  -0.347   0.256                 
un07  0.192   0.641  -0.115  -0.172           0.113 
un08 -0.114   0.817                   0.113         
un09          0.646  -0.101                   0.212 
un10  0.219   0.698  -0.212                         
un11          0.803          -0.103                 
un12 -0.180   0.740   0.166                         

               Factor1 Factor2 Factor3 Factor4 Factor5 Factor6
SS loadings      7.535   6.547   6.389   3.041   2.823   2.419
Proportion Var   0.122   0.106   0.103   0.049   0.046   0.039
Cumulative Var   0.122   0.227   0.330   0.379   0.425   0.464

kable(
  sort(efa_6f_pm$uniquenesses, decreasing = TRUE),
  col.names = "U")

	U
de11	0.7817421
pr04	0.7700534
pr10	0.7616189
ut04	0.7559106
fa03	0.7134353
de01	0.7002496
fa07	0.6907293
pr09	0.6888357
un06	0.6751271
pr02	0.6694849
pr06	0.6576002
ut07	0.6510578
co04	0.6481729
co06	0.6474121
de03	0.6464066
un03	0.6402866
pr03	0.6384384
co03	0.6327467
co10	0.6282188
de07	0.6246089
fa04	0.6137315
ut08	0.5910384
ut05	0.5868681
ut09	0.5865585
de08	0.5858475
de09	0.5766570
co08	0.5671255
co02	0.5579891
de05	0.5437340
fa10	0.5420869
ut12	0.5382611
fa08	0.5284220
de02	0.5246474
co09	0.5063667
pr07	0.4996945
pr08	0.4983024
ut03	0.4937529
de10	0.4934491
un09	0.4875879
fa09	0.4737183
fa02	0.4731288
fa06	0.4702934
un04	0.4642368
co01	0.4635405
un07	0.4574466
co05	0.4479825
ut06	0.4362455
un10	0.4358851
un12	0.4312571
pr01	0.4144342
ut11	0.4071750
un08	0.4066783
un11	0.3931924
fa01	0.3816574
un01	0.3730108
fa05	0.3486393
pr05	0.3357658
ut01	0.3321338
un05	0.3254634
de06	0.3122163
un02	0.3085120
ut02	0.3006345

5 factors, varimax rotation

efa_5f_vm <- factanal(taia %>% select(all_of(taia_items)),
                   factors = 5,
                   scores = "regression",
                   rotation = "varimax")

loadings(efa_5f_vm)

Loadings:
     Factor1 Factor2 Factor3 Factor4 Factor5
pr01  0.576   0.372   0.170   0.212         
pr02  0.319   0.359   0.221   0.205         
pr03  0.306  -0.108           0.412   0.121 
pr04  0.131  -0.197           0.340   0.154 
pr05  0.211   0.453   0.156   0.482         
pr06  0.501   0.249   0.142   0.100         
pr07  0.456   0.465           0.232         
pr08  0.567   0.334   0.123   0.160         
pr09  0.424   0.257   0.129   0.129         
pr10  0.369   0.262   0.124   0.104         
co01  0.303   0.625                   0.130 
co02  0.235   0.573   0.114           0.112 
co03  0.462   0.329           0.176         
co04  0.573           0.115                 
co05  0.197   0.690                         
co06  0.207   0.520                         
co08 -0.157   0.505  -0.112  -0.326  -0.146 
co09  0.121   0.681          -0.100         
co10  0.219   0.513   0.206  -0.125         
ut01  0.788                                 
ut02  0.792           0.100   0.136         
ut03  0.531  -0.225           0.358   0.140 
ut04  0.437                   0.115         
ut05  0.586   0.191                         
ut06  0.713   0.148                         
ut07  0.559   0.171                         
ut08  0.612   0.179                         
ut09  0.601   0.152           0.128         
ut11  0.362   0.341   0.171   0.431         
ut12  0.632   0.179   0.131   0.115         
fa01  0.317   0.338           0.123   0.618 
fa02                 -0.206   0.202   0.659 
fa03 -0.148   0.484          -0.103         
fa04          0.616                         
fa05  0.305   0.412                   0.604 
fa06  0.366   0.528   0.127   0.241   0.179 
fa07                          0.512   0.182 
fa08                 -0.190   0.284   0.591 
fa09                 -0.155   0.321   0.632 
fa10  0.278   0.126                   0.611 
de01  0.320   0.386   0.159                 
de02  0.282   0.553   0.132   0.281         
de03  0.246   0.493   0.117   0.176   0.105 
de05  0.583           0.133   0.230         
de06  0.219   0.462   0.197   0.470         
de07  0.462   0.290   0.220   0.182         
de08  0.392   0.386   0.195   0.273         
de09  0.367                   0.374         
de10  0.300   0.558           0.303   0.121 
de11                          0.445   0.153 
un01  0.301           0.727                 
un02          0.124   0.815                 
un03  0.221           0.501          -0.243 
un04  0.107   0.116   0.712                 
un05  0.219           0.787                 
un06                  0.519   0.148         
un07          0.328   0.651                 
un08  0.195           0.744                 
un09          0.198   0.667   0.124  -0.110 
un10          0.272   0.692          -0.101 
un11          0.107   0.764                 
un12  0.242           0.712                 

               Factor1 Factor2 Factor3 Factor4 Factor5
SS loadings      8.695   6.882   6.542   2.836   2.744
Proportion Var   0.140   0.111   0.106   0.046   0.044
Cumulative Var   0.140   0.251   0.357   0.403   0.447

kable(
  sort(efa_5f_vm$uniquenesses, decreasing = TRUE),
  col.names = "U"
)

	U
pr04	0.8036037
ut04	0.7875168
de11	0.7660851
pr10	0.7648954
fa03	0.7322846
pr09	0.7157810
de09	0.7138430
de01	0.7115636
pr03	0.7071547
un06	0.6984492
fa07	0.6934404
pr02	0.6780781
co06	0.6691958
pr06	0.6557484
ut07	0.6500545
co04	0.6435044
de03	0.6411034
un03	0.6404520
co03	0.6336224
co10	0.6291329
de07	0.6207641
ut05	0.6108805
fa04	0.6096628
ut09	0.5950296
co02	0.5895055
ut08	0.5880908
de05	0.5859234
co08	0.5800904
de08	0.5776240
ut12	0.5381209
ut11	0.5378917
fa10	0.5312032
fa08	0.5256412
pr08	0.5255447
ut03	0.5181711
de02	0.5158859
co09	0.5114014
pr07	0.5096638
co01	0.4937745
pr05	0.4926627
de10	0.4869821
un09	0.4861097
fa06	0.4806029
co05	0.4747549
fa09	0.4734086
fa02	0.4713133
de06	0.4691654
un04	0.4646410
un07	0.4595727
ut06	0.4594009
pr01	0.4496805
un10	0.4361787
un12	0.4325425
un08	0.4008023
un11	0.3971241
fa01	0.3854741
ut01	0.3691461
un01	0.3671937
fa05	0.3613714
ut02	0.3407660
un05	0.3303704
un02	0.3106689

5 factors, promax rotation

efa_5f_pm <- factanal(taia %>% select(all_of(taia_items)),
                   factors = 5,
                   scores = "regression",
                   rotation = "promax")

loadings(efa_5f_pm)

Loadings:
     Factor1 Factor2 Factor3 Factor4 Factor5
pr01  0.446   0.279           0.163         
pr02  0.143   0.296   0.114   0.211         
pr03  0.233  -0.214  -0.117   0.424         
pr04         -0.293           0.354   0.107 
pr05 -0.115   0.392           0.579         
pr06  0.456   0.170                         
pr07  0.281   0.412           0.218         
pr08  0.480   0.250           0.106         
pr09  0.342   0.189                         
pr10  0.300   0.206                  -0.112 
co01  0.146   0.650                   0.122 
co02          0.599                   0.111 
co03  0.354   0.265           0.139         
co04  0.624                                 
co05          0.759          -0.112         
co06          0.545                  -0.122 
co08 -0.181   0.655  -0.178  -0.313  -0.109 
co09          0.763  -0.105  -0.100         
co10  0.114   0.531   0.122  -0.157         
ut01  0.932  -0.173          -0.161         
ut02  0.859  -0.129                         
ut03  0.556  -0.375           0.303         
ut04  0.452                                 
ut05  0.610   0.111                         
ut06  0.757                                 
ut07  0.631   0.114          -0.191         
ut08  0.655                  -0.102         
ut09  0.605                                 
ut11  0.121   0.247           0.486         
ut12  0.625                                 
fa01  0.152   0.310   0.125           0.634 
fa02 -0.203                   0.143   0.681 
fa03 -0.291   0.581                         
fa04 -0.281   0.695                         
fa05  0.129   0.400                   0.620 
fa06  0.134   0.490           0.229   0.130 
fa07 -0.104                   0.583   0.102 
fa08 -0.210                   0.254   0.592 
fa09 -0.158                   0.280   0.627 
fa10  0.247   0.110          -0.175   0.648 
de01  0.200   0.356                         
de02          0.524           0.319         
de03          0.478           0.183         
de05  0.562                   0.179         
de06 -0.118   0.396           0.550         
de07  0.346   0.199   0.104   0.156         
de08  0.192   0.310           0.272         
de09  0.305  -0.213           0.381         
de10          0.534           0.332         
de11                 -0.110   0.509         
un01  0.258  -0.197   0.810  -0.169   0.132 
un02                  0.857                 
un03  0.185           0.450          -0.246 
un04                  0.739                 
un05  0.103  -0.121   0.847                 
un06 -0.250  -0.119   0.556   0.200         
un07 -0.175   0.266   0.641                 
un08  0.101  -0.128   0.827  -0.111   0.126 
un09 -0.166           0.647   0.170         
un10 -0.202   0.204   0.699                 
un11                  0.805                 
un12  0.151  -0.155   0.746                 

               Factor1 Factor2 Factor3 Factor4 Factor5
SS loadings      7.635   6.936   6.600   3.174   2.713
Proportion Var   0.123   0.112   0.106   0.051   0.044
Cumulative Var   0.123   0.235   0.341   0.393   0.436

kable(
  sort(efa_5f_pm$uniquenesses, decreasing = TRUE),
  col.names = "U"
)

	U
pr04	0.8036037
ut04	0.7875168
de11	0.7660851
pr10	0.7648954
fa03	0.7322846
pr09	0.7157810
de09	0.7138430
de01	0.7115636
pr03	0.7071547
un06	0.6984492
fa07	0.6934404
pr02	0.6780781
co06	0.6691958
pr06	0.6557484
ut07	0.6500545
co04	0.6435044
de03	0.6411034
un03	0.6404520
co03	0.6336224
co10	0.6291329
de07	0.6207641
ut05	0.6108805
fa04	0.6096628
ut09	0.5950296
co02	0.5895055
ut08	0.5880908
de05	0.5859234
co08	0.5800904
de08	0.5776240
ut12	0.5381209
ut11	0.5378917
fa10	0.5312032
fa08	0.5256412
pr08	0.5255447
ut03	0.5181711
de02	0.5158859
co09	0.5114014
pr07	0.5096638
co01	0.4937745
pr05	0.4926627
de10	0.4869821
un09	0.4861097
fa06	0.4806029
co05	0.4747549
fa09	0.4734086
fa02	0.4713133
de06	0.4691654
un04	0.4646410
un07	0.4595727
ut06	0.4594009
pr01	0.4496805
un10	0.4361787
un12	0.4325425
un08	0.4008023
un11	0.3971241
fa01	0.3854741
ut01	0.3691461
un01	0.3671937
fa05	0.3613714
ut02	0.3407660
un05	0.3303704
un02	0.3106689

Confirmatory Factor Analysis

Basic model

Model:

mdl1 <- "
PR =~ pr01 + pr02 + pr03 + pr04 + pr05 + pr06 + pr07 + pr08 + pr09 + pr10
CO =~ co01 + co02 + co03 + co04 + co05 + co06 + co08 + co09 + co10
UT =~ ut01 + ut02 + ut03 + ut04 + ut05 + ut06 + ut07 + ut08 + ut09 + ut11 + ut12
FA =~ fa01 + fa02 + fa03 + fa04 + fa05 + fa06 + fa07 + fa08 + fa09 + fa10
DE =~ de01 + de02 + de03 + de05 + de06 + de07 + de08 + de09 + de10 + de11
UN =~ un01 + un02 + un03 + un04 + un05 + un06 + un07 + un08 + un09 + un10 + un11 + un12
"

CFA model fitting:

model1 <- cfa(mdl1, taia %>% select(all_of(taia_items)))

summary(model1)

lavaan 0.6-8 ended normally after 62 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                       139
                                                      
  Number of observations                           495
                                                      
Model Test User Model:
                                                      
  Test statistic                              6326.223
  Degrees of freedom                              1814
  P-value (Chi-square)                           0.000

Parameter Estimates:

  Standard errors                             Standard
  Information                                 Expected
  Information saturated (h1) model          Structured

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  PR =~                                               
    pr01              1.000                           
    pr02              0.727    0.055   13.199    0.000
    pr03              0.386    0.060    6.384    0.000
    pr04              0.153    0.063    2.431    0.015
    pr05              0.870    0.068   12.721    0.000
    pr06              0.808    0.061   13.285    0.000
    pr07              1.040    0.061   17.095    0.000
    pr08              0.847    0.050   17.029    0.000
    pr09              0.714    0.054   13.167    0.000
    pr10              0.666    0.060   11.105    0.000
  CO =~                                               
    co01              1.000                           
    co02              0.896    0.061   14.596    0.000
    co03              0.646    0.061   10.618    0.000
    co04              0.459    0.065    7.065    0.000
    co05              1.090    0.065   16.652    0.000
    co06              0.856    0.066   13.052    0.000
    co08              0.438    0.062    7.047    0.000
    co09              0.978    0.063   15.527    0.000
    co10              0.831    0.065   12.804    0.000
  UT =~                                               
    ut01              1.000                           
    ut02              1.083    0.055   19.815    0.000
    ut03              0.682    0.062   11.048    0.000
    ut04              0.636    0.062   10.244    0.000
    ut05              0.965    0.066   14.724    0.000
    ut06              1.008    0.058   17.348    0.000
    ut07              0.790    0.062   12.676    0.000
    ut08              0.807    0.057   14.082    0.000
    ut09              0.945    0.063   14.930    0.000
    ut11              0.789    0.068   11.527    0.000
    ut12              0.974    0.062   15.791    0.000
  FA =~                                               
    fa01              1.000                           
    fa02              0.535    0.060    8.869    0.000
    fa03              0.219    0.060    3.670    0.000
    fa04              0.424    0.056    7.575    0.000
    fa05              1.028    0.051   20.280    0.000
    fa06              0.716    0.053   13.558    0.000
    fa07              0.335    0.057    5.911    0.000
    fa08              0.487    0.058    8.366    0.000
    fa09              0.626    0.059   10.519    0.000
    fa10              0.785    0.059   13.357    0.000
  DE =~                                               
    de01              1.000                           
    de02              1.315    0.113   11.688    0.000
    de03              1.183    0.111   10.668    0.000
    de05              0.981    0.103    9.509    0.000
    de06              1.276    0.116   11.019    0.000
    de07              0.979    0.093   10.586    0.000
    de08              1.185    0.102   11.579    0.000
    de09              0.604    0.098    6.189    0.000
    de10              1.377    0.116   11.853    0.000
    de11              0.476    0.096    4.958    0.000
  UN =~                                               
    un01              1.000                           
    un02              1.215    0.064   18.860    0.000
    un03              0.817    0.068   11.959    0.000
    un04              1.025    0.062   16.485    0.000
    un05              1.142    0.063   18.233    0.000
    un06              0.783    0.072   10.830    0.000
    un07              1.040    0.068   15.336    0.000
    un08              1.120    0.066   16.897    0.000
    un09              1.090    0.071   15.404    0.000
    un10              1.050    0.066   15.883    0.000
    un11              1.192    0.069   17.382    0.000
    un12              1.065    0.064   16.524    0.000

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  PR ~~                                               
    CO                0.417    0.043    9.702    0.000
    UT                0.479    0.045   10.634    0.000
    FA                0.402    0.044    9.066    0.000
    DE                0.423    0.045    9.495    0.000
    UN                0.232    0.034    6.779    0.000
  CO ~~                                               
    UT                0.280    0.038    7.332    0.000
    FA                0.355    0.044    8.018    0.000
    DE                0.326    0.039    8.350    0.000
    UN                0.171    0.033    5.125    0.000
  UT ~~                                               
    FA                0.331    0.043    7.706    0.000
    DE                0.341    0.040    8.621    0.000
    UN                0.187    0.034    5.560    0.000
  FA ~~                                               
    DE                0.366    0.043    8.534    0.000
    UN                0.061    0.035    1.738    0.082
  DE ~~                                               
    UN                0.186    0.029    6.327    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .pr01              0.366    0.028   13.060    0.000
   .pr02              0.619    0.041   14.916    0.000
   .pr03              0.936    0.060   15.582    0.000
   .pr04              1.071    0.068   15.711    0.000
   .pr05              0.977    0.065   14.993    0.000
   .pr06              0.751    0.050   14.902    0.000
   .pr07              0.581    0.042   13.928    0.000
   .pr08              0.390    0.028   13.953    0.000
   .pr09              0.601    0.040   14.921    0.000
   .pr10              0.805    0.053   15.208    0.000
   .co01              0.526    0.040   13.135    0.000
   .co02              0.573    0.041   13.824    0.000
   .co03              0.780    0.052   15.010    0.000
   .co04              1.045    0.068   15.460    0.000
   .co05              0.481    0.039   12.355    0.000
   .co06              0.763    0.053   14.429    0.000
   .co08              0.957    0.062   15.462    0.000
   .co09              0.536    0.040   13.296    0.000
   .co10              0.763    0.053   14.505    0.000
   .ut01              0.443    0.033   13.514    0.000
   .ut02              0.333    0.027   12.266    0.000
   .ut03              0.918    0.060   15.239    0.000
   .ut04              0.959    0.063   15.322    0.000
   .ut05              0.844    0.058   14.654    0.000
   .ut06              0.528    0.038   13.844    0.000
   .ut07              0.866    0.058   15.029    0.000
   .ut08              0.674    0.046   14.788    0.000
   .ut09              0.776    0.053   14.606    0.000
   .ut11              1.107    0.073   15.183    0.000
   .ut12              0.689    0.048   14.384    0.000
   .fa01              0.393    0.036   11.016    0.000
   .fa02              1.156    0.076   15.296    0.000
   .fa03              1.245    0.079   15.664    0.000
   .fa04              1.028    0.067   15.424    0.000
   .fa05              0.348    0.034   10.153    0.000
   .fa06              0.744    0.051   14.506    0.000
   .fa07              1.092    0.070   15.551    0.000
   .fa08              1.094    0.071   15.349    0.000
   .fa09              1.071    0.071   15.086    0.000
   .fa10              0.932    0.064   14.555    0.000
   .de01              0.822    0.055   14.942    0.000
   .de02              0.678    0.048   14.054    0.000
   .de03              0.895    0.061   14.713    0.000
   .de05              0.985    0.065   15.098    0.000
   .de06              0.891    0.061   14.538    0.000
   .de07              0.636    0.043   14.749    0.000
   .de08              0.583    0.041   14.151    0.000
   .de09              1.297    0.083   15.551    0.000
   .de10              0.678    0.049   13.889    0.000
   .de11              1.361    0.087   15.625    0.000
   .un01              0.500    0.035   14.388    0.000
   .un02              0.399    0.030   13.239    0.000
   .un03              0.962    0.063   15.267    0.000
   .un04              0.541    0.037   14.425    0.000
   .un05              0.425    0.031   13.665    0.000
   .un06              1.147    0.075   15.374    0.000
   .un07              0.729    0.049   14.737    0.000
   .un08              0.583    0.041   14.285    0.000
   .un09              0.789    0.054   14.721    0.000
   .un10              0.655    0.045   14.601    0.000
   .un11              0.583    0.041   14.094    0.000
   .un12              0.578    0.040   14.413    0.000
    PR                0.605    0.059   10.207    0.000
    CO                0.633    0.069    9.144    0.000
    UT                0.659    0.066    9.942    0.000
    FA                0.816    0.077   10.599    0.000
    DE                0.377    0.058    6.490    0.000
    UN                0.604    0.064    9.418    0.000

Fit measures:

kable(tibble(
  `Model 1` = c(
    "Chi-Squared",
    "DF",
    "p",
    "GFI",
    "AGFI",
    "CFI",
    "TLI",
    "SRMR",
    "RMSEA"
  ),
  Value = round(fitmeasures(
    model1,
    c(
      "chisq",
      "df",
      "pvalue",
      "gfi",
      "agfi",
      "cfi",
      "tli",
      "srmr",
      "rmsea"
    )
  ), 4)
))

Model 1	Value
Chi-Squared	6326.2235
DF	1814.0000
p	0.0000
GFI	0.6381
AGFI	0.6104
CFI	0.7096
TLI	0.6973
SRMR	0.1010
RMSEA	0.0709

Standardized solution:

smodel1 <- standardizedsolution(model1)

Loadings:

kable(
  smodel1 %>%
    filter(op == "=~"),
  col.names = c(
    "Factor",
    "",
    "Item",
    "Loading",
    "SE",
    "z",
    "p",
    "CI lower bound",
    "CI upper bound"
  ),
  digits = 3
)

Factor		Item	Loading	SE	z	p	CI lower bound	CI upper bound
PR	=~	pr01	0.789	0.020	39.913	0.000	0.751	0.828
PR	=~	pr02	0.584	0.032	18.261	0.000	0.521	0.647
PR	=~	pr03	0.296	0.043	6.854	0.000	0.211	0.381
PR	=~	pr04	0.114	0.047	2.456	0.014	0.023	0.206
PR	=~	pr05	0.565	0.033	17.164	0.000	0.501	0.630
PR	=~	pr06	0.587	0.032	18.467	0.000	0.525	0.650
PR	=~	pr07	0.728	0.024	30.723	0.000	0.682	0.775
PR	=~	pr08	0.726	0.024	30.439	0.000	0.679	0.773
PR	=~	pr09	0.583	0.032	18.186	0.000	0.520	0.645
PR	=~	pr10	0.500	0.036	13.888	0.000	0.429	0.570
CO	=~	co01	0.739	0.024	30.666	0.000	0.692	0.786
CO	=~	co02	0.686	0.027	25.127	0.000	0.632	0.739
CO	=~	co03	0.503	0.037	13.698	0.000	0.431	0.575
CO	=~	co04	0.337	0.043	7.853	0.000	0.253	0.421
CO	=~	co05	0.781	0.022	36.274	0.000	0.739	0.823
CO	=~	co06	0.615	0.031	19.688	0.000	0.554	0.676
CO	=~	co08	0.336	0.043	7.829	0.000	0.252	0.420
CO	=~	co09	0.728	0.025	29.429	0.000	0.680	0.777
CO	=~	co10	0.604	0.032	18.958	0.000	0.541	0.666
UT	=~	ut01	0.773	0.021	37.597	0.000	0.733	0.814
UT	=~	ut02	0.836	0.016	51.142	0.000	0.804	0.868
UT	=~	ut03	0.500	0.036	13.954	0.000	0.430	0.570
UT	=~	ut04	0.466	0.037	12.493	0.000	0.393	0.539
UT	=~	ut05	0.649	0.028	22.945	0.000	0.593	0.704
UT	=~	ut06	0.748	0.022	33.612	0.000	0.704	0.791
UT	=~	ut07	0.568	0.033	17.378	0.000	0.504	0.632
UT	=~	ut08	0.624	0.030	21.010	0.000	0.566	0.682
UT	=~	ut09	0.657	0.028	23.611	0.000	0.602	0.711
UT	=~	ut11	0.520	0.035	14.890	0.000	0.452	0.589
UT	=~	ut12	0.690	0.026	26.662	0.000	0.639	0.741
FA	=~	fa01	0.822	0.019	42.299	0.000	0.784	0.860
FA	=~	fa02	0.410	0.040	10.123	0.000	0.330	0.489
FA	=~	fa03	0.175	0.047	3.752	0.000	0.083	0.266
FA	=~	fa04	0.353	0.042	8.337	0.000	0.270	0.436
FA	=~	fa05	0.844	0.018	46.444	0.000	0.809	0.880
FA	=~	fa06	0.600	0.032	18.680	0.000	0.537	0.663
FA	=~	fa07	0.279	0.044	6.264	0.000	0.191	0.366
FA	=~	fa08	0.388	0.041	9.407	0.000	0.307	0.469
FA	=~	fa09	0.479	0.038	12.693	0.000	0.405	0.553
FA	=~	fa10	0.592	0.033	18.218	0.000	0.528	0.656
DE	=~	de01	0.561	0.033	16.808	0.000	0.495	0.626
DE	=~	de02	0.700	0.026	27.265	0.000	0.650	0.751
DE	=~	de03	0.609	0.031	19.717	0.000	0.548	0.670
DE	=~	de05	0.519	0.035	14.677	0.000	0.450	0.588
DE	=~	de06	0.639	0.029	21.837	0.000	0.582	0.696
DE	=~	de07	0.602	0.031	19.273	0.000	0.541	0.663
DE	=~	de08	0.690	0.026	26.215	0.000	0.638	0.741
DE	=~	de09	0.310	0.043	7.191	0.000	0.225	0.394
DE	=~	de10	0.716	0.025	29.002	0.000	0.668	0.765
DE	=~	de11	0.243	0.045	5.436	0.000	0.155	0.331
UN	=~	un01	0.740	0.022	33.462	0.000	0.696	0.783
UN	=~	un02	0.831	0.016	52.491	0.000	0.800	0.862
UN	=~	un03	0.544	0.033	16.332	0.000	0.478	0.609
UN	=~	un04	0.735	0.022	32.798	0.000	0.691	0.779
UN	=~	un05	0.806	0.018	45.760	0.000	0.771	0.840
UN	=~	un06	0.494	0.036	13.895	0.000	0.425	0.564
UN	=~	un07	0.687	0.025	27.059	0.000	0.638	0.737
UN	=~	un08	0.752	0.021	35.289	0.000	0.710	0.794
UN	=~	un09	0.690	0.025	27.358	0.000	0.641	0.740
UN	=~	un10	0.710	0.024	29.592	0.000	0.663	0.757
UN	=~	un11	0.772	0.020	38.620	0.000	0.732	0.811
UN	=~	un12	0.737	0.022	33.023	0.000	0.693	0.780

Covariances:

kable(
  smodel1 %>% 
    filter(op == "~~" & lhs != rhs),
  col.names = c("Factor", "", "Factor", "Covariance", "SE", "z", "p", "CI lower bound", "CI upper bound"),
  digits = 3
)

Factor		Factor	Covariance	SE	z	p	CI lower bound	CI upper bound
PR	~~	CO	0.674	0.032	21.123	0.000	0.611	0.736
PR	~~	UT	0.758	0.025	29.745	0.000	0.708	0.808
PR	~~	FA	0.572	0.037	15.251	0.000	0.498	0.645
PR	~~	DE	0.886	0.019	47.788	0.000	0.849	0.922
PR	~~	UN	0.383	0.043	8.811	0.000	0.298	0.469
CO	~~	UT	0.434	0.042	10.255	0.000	0.351	0.517
CO	~~	FA	0.493	0.041	12.022	0.000	0.413	0.574
CO	~~	DE	0.667	0.033	20.416	0.000	0.603	0.731
CO	~~	UN	0.276	0.047	5.929	0.000	0.185	0.367
UT	~~	FA	0.451	0.042	10.813	0.000	0.369	0.532
UT	~~	DE	0.684	0.030	22.435	0.000	0.624	0.744
UT	~~	UN	0.296	0.045	6.570	0.000	0.207	0.384
FA	~~	DE	0.659	0.033	19.845	0.000	0.594	0.724
FA	~~	UN	0.087	0.050	1.762	0.078	-0.010	0.185
DE	~~	UN	0.389	0.044	8.920	0.000	0.304	0.475

Residuals:

kable(
  smodel1 %>% 
    filter(op == "~~" & lhs == rhs)%>% 
    select(-(2:3)),
  col.names = c("Item", "Residual", "SE", "z", "p", "CI lower bound", "CI upper bound"),
  digits = 3
)

Item	Residual	SE	z	p	CI lower bound	CI upper bound
pr01	0.377	0.031	12.076	0	0.316	0.438
pr02	0.659	0.037	17.653	0	0.586	0.732
pr03	0.912	0.026	35.640	0	0.862	0.962
pr04	0.987	0.011	92.749	0	0.966	1.008
pr05	0.681	0.037	18.291	0	0.608	0.754
pr06	0.655	0.037	17.542	0	0.582	0.728
pr07	0.470	0.035	13.609	0	0.402	0.537
pr08	0.473	0.035	13.667	0	0.405	0.541
pr09	0.661	0.037	17.694	0	0.587	0.734
pr10	0.750	0.036	20.839	0	0.680	0.821
co01	0.454	0.036	12.730	0	0.384	0.523
co02	0.530	0.037	14.153	0	0.456	0.603
co03	0.747	0.037	20.238	0	0.675	0.820
co04	0.887	0.029	30.728	0	0.830	0.943
co05	0.390	0.034	11.593	0	0.324	0.456
co06	0.622	0.038	16.181	0	0.546	0.697
co08	0.887	0.029	30.806	0	0.831	0.944
co09	0.469	0.036	13.014	0	0.399	0.540
co10	0.636	0.038	16.536	0	0.560	0.711
ut01	0.402	0.032	12.630	0	0.340	0.464
ut02	0.301	0.027	11.006	0	0.247	0.354
ut03	0.750	0.036	20.907	0	0.679	0.820
ut04	0.783	0.035	22.500	0	0.715	0.851
ut05	0.579	0.037	15.774	0	0.507	0.651
ut06	0.441	0.033	13.251	0	0.376	0.506
ut07	0.678	0.037	18.290	0	0.605	0.751
ut08	0.611	0.037	16.492	0	0.538	0.683
ut09	0.568	0.037	15.554	0	0.497	0.640
ut11	0.729	0.036	20.063	0	0.658	0.801
ut12	0.524	0.036	14.683	0	0.454	0.594
fa01	0.325	0.032	10.177	0	0.262	0.387
fa02	0.832	0.033	25.070	0	0.767	0.897
fa03	0.969	0.016	59.581	0	0.938	1.001
fa04	0.875	0.030	29.210	0	0.816	0.934
fa05	0.287	0.031	9.357	0	0.227	0.347
fa06	0.640	0.039	16.624	0	0.565	0.716
fa07	0.922	0.025	37.218	0	0.874	0.971
fa08	0.849	0.032	26.527	0	0.787	0.912
fa09	0.770	0.036	21.268	0	0.699	0.841
fa10	0.649	0.038	16.872	0	0.574	0.725
de01	0.686	0.037	18.318	0	0.612	0.759
de02	0.510	0.036	14.162	0	0.439	0.580
de03	0.629	0.038	16.722	0	0.555	0.703
de05	0.731	0.037	19.910	0	0.659	0.803
de06	0.592	0.037	15.832	0	0.519	0.665
de07	0.637	0.038	16.934	0	0.564	0.711
de08	0.524	0.036	14.436	0	0.453	0.595
de09	0.904	0.027	33.919	0	0.852	0.956
de10	0.487	0.035	13.746	0	0.417	0.556
de11	0.941	0.022	43.330	0	0.898	0.984
un01	0.453	0.033	13.854	0	0.389	0.517
un02	0.309	0.026	11.747	0	0.258	0.361
un03	0.705	0.036	19.471	0	0.634	0.775
un04	0.460	0.033	13.962	0	0.395	0.524
un05	0.350	0.028	12.343	0	0.295	0.406
un06	0.756	0.035	21.495	0	0.687	0.825
un07	0.528	0.035	15.106	0	0.459	0.596
un08	0.435	0.032	13.574	0	0.372	0.498
un09	0.524	0.035	15.035	0	0.455	0.592
un10	0.496	0.034	14.549	0	0.429	0.563
un11	0.405	0.031	13.125	0	0.344	0.465
un12	0.458	0.033	13.925	0	0.393	0.522
PR	1.000	0.000	NA	NA	1.000	1.000
CO	1.000	0.000	NA	NA	1.000	1.000
UT	1.000	0.000	NA	NA	1.000	1.000
FA	1.000	0.000	NA	NA	1.000	1.000
DE	1.000	0.000	NA	NA	1.000	1.000
UN	1.000	0.000	NA	NA	1.000	1.000

Visualization:

semPaths(model1, "std")

Model with general factor

Model:

mdl2 <- "
PR =~ pr01 + pr02 + pr03 + pr04 + pr05 + pr06 + pr07 + pr08 + pr09 + pr10
CO =~ co01 + co02 + co03 + co04 + co05 + co06 + co08 + co09 + co10
UT =~ ut01 + ut02 + ut03 + ut04 + ut05 + ut06 + ut07 + ut08 + ut09 + ut11 + ut12
FA =~ fa01 + fa02 + fa03 + fa04 + fa05 + fa06 + fa07 + fa08 + fa09 + fa10
DE =~ de01 + de02 + de03 + de05 + de06 + de07 + de08 + de09 + de10 + de11
UN =~ un01 + un02 + un03 + un04 + un05 + un06 + un07 + un08 + un09 + un10 + un11 + un12
DigTrust =~ PR + CO + UT + FA + DE + UN
"

model2 <- cfa(mdl2, taia %>% select(all_of(taia_items)))

summary(model2)

lavaan 0.6-8 ended normally after 44 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                       130
                                                      
  Number of observations                           495
                                                      
Model Test User Model:
                                                      
  Test statistic                              6381.193
  Degrees of freedom                              1823
  P-value (Chi-square)                           0.000

Parameter Estimates:

  Standard errors                             Standard
  Information                                 Expected
  Information saturated (h1) model          Structured

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  PR =~                                               
    pr01              1.000                           
    pr02              0.732    0.055   13.227    0.000
    pr03              0.389    0.061    6.409    0.000
    pr04              0.160    0.063    2.533    0.011
    pr05              0.882    0.069   12.845    0.000
    pr06              0.797    0.061   13.006    0.000
    pr07              1.049    0.061   17.137    0.000
    pr08              0.846    0.050   16.877    0.000
    pr09              0.719    0.055   13.186    0.000
    pr10              0.661    0.060   10.962    0.000
  CO =~                                               
    co01              1.000                           
    co02              0.894    0.062   14.491    0.000
    co03              0.652    0.061   10.699    0.000
    co04              0.473    0.065    7.263    0.000
    co05              1.088    0.066   16.548    0.000
    co06              0.862    0.066   13.089    0.000
    co08              0.435    0.062    6.976    0.000
    co09              0.977    0.063   15.442    0.000
    co10              0.834    0.065   12.798    0.000
  UT =~                                               
    ut01              1.000                           
    ut02              1.080    0.055   19.757    0.000
    ut03              0.674    0.062   10.910    0.000
    ut04              0.635    0.062   10.237    0.000
    ut05              0.972    0.065   14.837    0.000
    ut06              1.007    0.058   17.336    0.000
    ut07              0.791    0.062   12.699    0.000
    ut08              0.807    0.057   14.089    0.000
    ut09              0.946    0.063   14.941    0.000
    ut11              0.790    0.068   11.534    0.000
    ut12              0.973    0.062   15.774    0.000
  FA =~                                               
    fa01              1.000                           
    fa02              0.522    0.060    8.760    0.000
    fa03              0.204    0.059    3.452    0.001
    fa04              0.407    0.055    7.352    0.000
    fa05              1.017    0.050   20.447    0.000
    fa06              0.704    0.052   13.544    0.000
    fa07              0.323    0.056    5.749    0.000
    fa08              0.475    0.058    8.239    0.000
    fa09              0.616    0.059   10.488    0.000
    fa10              0.780    0.058   13.496    0.000
  DE =~                                               
    de01              1.000                           
    de02              1.314    0.113   11.628    0.000
    de03              1.176    0.111   10.576    0.000
    de05              1.006    0.104    9.645    0.000
    de06              1.267    0.116   10.914    0.000
    de07              0.989    0.093   10.609    0.000
    de08              1.188    0.103   11.539    0.000
    de09              0.623    0.098    6.342    0.000
    de10              1.371    0.117   11.764    0.000
    de11              0.475    0.096    4.934    0.000
  UN =~                                               
    un01              1.000                           
    un02              1.212    0.064   18.935    0.000
    un03              0.811    0.068   11.917    0.000
    un04              1.022    0.062   16.530    0.000
    un05              1.140    0.062   18.326    0.000
    un06              0.780    0.072   10.831    0.000
    un07              1.035    0.067   15.346    0.000
    un08              1.118    0.066   16.974    0.000
    un09              1.085    0.070   15.412    0.000
    un10              1.046    0.066   15.902    0.000
    un11              1.188    0.068   17.430    0.000
    un12              1.061    0.064   16.562    0.000
  DigTrust =~                                         
    PR                1.000                           
    CO                0.746    0.061   12.327    0.000
    UT                0.818    0.060   13.693    0.000
    FA                0.781    0.064   12.133    0.000
    DE                0.777    0.066   11.697    0.000
    UN                0.408    0.053    7.651    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .pr01              0.369    0.028   13.031    0.000
   .pr02              0.616    0.041   14.883    0.000
   .pr03              0.935    0.060   15.576    0.000
   .pr04              1.070    0.068   15.709    0.000
   .pr05              0.966    0.065   14.947    0.000
   .pr06              0.763    0.051   14.921    0.000
   .pr07              0.573    0.041   13.836    0.000
   .pr08              0.393    0.028   13.938    0.000
   .pr09              0.599    0.040   14.890    0.000
   .pr10              0.810    0.053   15.208    0.000
   .co01              0.528    0.040   13.119    0.000
   .co02              0.578    0.042   13.832    0.000
   .co03              0.775    0.052   14.982    0.000
   .co04              1.037    0.067   15.438    0.000
   .co05              0.485    0.039   12.362    0.000
   .co06              0.759    0.053   14.391    0.000
   .co08              0.959    0.062   15.463    0.000
   .co09              0.539    0.041   13.290    0.000
   .co10              0.761    0.053   14.482    0.000
   .ut01              0.442    0.033   13.486    0.000
   .ut02              0.336    0.027   12.276    0.000
   .ut03              0.925    0.061   15.248    0.000
   .ut04              0.959    0.063   15.318    0.000
   .ut05              0.836    0.057   14.615    0.000
   .ut06              0.528    0.038   13.826    0.000
   .ut07              0.864    0.058   15.017    0.000
   .ut08              0.673    0.046   14.776    0.000
   .ut09              0.775    0.053   14.590    0.000
   .ut11              1.106    0.073   15.176    0.000
   .ut12              0.690    0.048   14.373    0.000
   .fa01              0.375    0.035   10.619    0.000
   .fa02              1.162    0.076   15.307    0.000
   .fa03              1.250    0.080   15.672    0.000
   .fa04              1.036    0.067   15.443    0.000
   .fa05              0.348    0.035   10.076    0.000
   .fa06              0.748    0.052   14.517    0.000
   .fa07              1.097    0.070   15.560    0.000
   .fa08              1.100    0.072   15.361    0.000
   .fa09              1.074    0.071   15.090    0.000
   .fa10              0.927    0.064   14.529    0.000
   .de01              0.823    0.055   14.925    0.000
   .de02              0.681    0.049   14.028    0.000
   .de03              0.904    0.061   14.713    0.000
   .de05              0.968    0.064   15.039    0.000
   .de06              0.902    0.062   14.545    0.000
   .de07              0.630    0.043   14.698    0.000
   .de08              0.583    0.041   14.109    0.000
   .de09              1.288    0.083   15.533    0.000
   .de10              0.687    0.049   13.891    0.000
   .de11              1.361    0.087   15.623    0.000
   .un01              0.497    0.035   14.367    0.000
   .un02              0.399    0.030   13.228    0.000
   .un03              0.966    0.063   15.272    0.000
   .un04              0.541    0.038   14.422    0.000
   .un05              0.423    0.031   13.641    0.000
   .un06              1.148    0.075   15.374    0.000
   .un07              0.732    0.050   14.740    0.000
   .un08              0.581    0.041   14.271    0.000
   .un09              0.792    0.054   14.725    0.000
   .un10              0.657    0.045   14.604    0.000
   .un11              0.584    0.041   14.091    0.000
   .un12              0.578    0.040   14.412    0.000
   .PR                0.051    0.017    2.954    0.003
   .CO                0.324    0.039    8.231    0.000
   .UT                0.290    0.033    8.734    0.000
   .FA                0.498    0.051    9.744    0.000
   .DE                0.043    0.012    3.438    0.001
   .UN                0.516    0.055    9.336    0.000
    DigTrust          0.552    0.058    9.531    0.000

kable(tibble(
  `Model 2` = c(
    "Chi-Squared",
    "DF",
    "p",
    "GFI",
    "AGFI",
    "CFI",
    "TLI",
    "SRMR",
    "RMSEA"
  ),
  Value = round(fitmeasures(
    model2,
    c(
      "chisq",
      "df",
      "pvalue",
      "gfi",
      "agfi",
      "cfi",
      "tli",
      "srmr",
      "rmsea"
    )
  ), 4)
))

Model 2	Value
Chi-Squared	6381.1932
DF	1823.0000
p	0.0000
GFI	0.6329
AGFI	0.6068
CFI	0.7067
TLI	0.6957
SRMR	0.1029
RMSEA	0.0711

semPaths(model2, "std")

Validation

TAIA total score

taia %>% 
  select(id, all_of(taia_items)) %>% 
  pivot_longer(all_of(taia_items),
               names_to = "subscale",
               values_to = "score") %>% 
  mutate(subscale = str_remove_all(subscale, "[:digit:]{2}") %>% toupper()) %>% 
  group_by(id, subscale) %>% 
  summarise(total_score = sum(score)) %>% 
  pivot_wider(id_cols = id,
              names_from = subscale,
              values_from = total_score) %>% 
  full_join(taia) -> taia

clrs <-
  c("darkred",
    "chocolate3",
    "goldenrod3",
    "darkgreen",
    "darkblue",
    "purple4")

Correlations with General Trust Scale

taia %>% 
  pivot_longer(cols = c("PR", "CO", "UT", "FA", "DE", "UN"),
               names_to = "subscale",
               values_to = "score") %>%
  mutate(subscale = factor(subscale, levels = c("PR", "CO", "UT", "FA", "DE", "UN"))) -> taia_l

taia_l %>% 
  ggplot(aes(score, gt_score, color = subscale)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm") +
  facet_wrap(~ subscale) +
  scale_color_manual(values = clrs) +
  guides(color = FALSE) +
  labs(x = "TAIA subscale total score",
       y = "General Trust Scale total score",
       title = "Corelations between General Trust and TAIA subscales") +
  theme(plot.title = element_text(hjust = .5))

cor.test(taia$PR, taia$gt_score)

    Pearson's product-moment correlation

data:  taia$PR and taia$gt_score
t = 3.1872, df = 493, p-value = 0.001528
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.05463758 0.22737163
sample estimates:
      cor 
0.1420861 

cor.test(taia$CO, taia$gt_score)

    Pearson's product-moment correlation

data:  taia$CO and taia$gt_score
t = 3.842, df = 493, p-value = 0.000138
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.08362567 0.25480562
sample estimates:
      cor 
0.1705018 

cor.test(taia$UT, taia$gt_score)

    Pearson's product-moment correlation

data:  taia$UT and taia$gt_score
t = 2.4679, df = 493, p-value = 0.01393
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.02255584 0.19668679
sample estimates:
     cor 
0.110469 

cor.test(taia$FA, taia$gt_score)

    Pearson's product-moment correlation

data:  taia$FA and taia$gt_score
t = 2.0938, df = 493, p-value = 0.03678
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.005800447 0.180524218
sample estimates:
      cor 
0.0938852 

cor.test(taia$DE, taia$gt_score)

    Pearson's product-moment correlation

data:  taia$DE and taia$gt_score
t = 4.1369, df = 493, p-value = 4.139e-05
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.09659152 0.26698780
sample estimates:
     cor 
0.183165 

cor.test(taia$UN, taia$gt_score)

    Pearson's product-moment correlation

data:  taia$UN and taia$gt_score
t = 3.5643, df = 493, p-value = 0.0004003
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.07136383 0.24323469
sample estimates:
      cor 
0.1584997 

Correlations with questions

taia_l %>% 
  ggplot(aes(score, n_dighelp, color = subscale)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm") +
  facet_wrap(~ subscale) +
  guides(color = FALSE) +
  scale_color_manual(values = clrs) +
  labs(x = "TAIA subscales total score",
       y = "Number of digital helpers",
       title = "Correlation TAIA subscales with number of digital helpers") +
  theme(plot.title = element_text(hjust = .5))

cor.test(taia$PR, taia$n_dighelp, method = "sp")

    Spearman's rank correlation rho

data:  taia$PR and taia$n_dighelp
S = 5561417, p-value = 0.01861
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1281319 

cor.test(taia$CO, taia$n_dighelp, method = "sp")

    Spearman's rank correlation rho

data:  taia$CO and taia$n_dighelp
S = 6618523, p-value = 0.4916
alternative hypothesis: true rho is not equal to 0
sample estimates:
        rho 
-0.03759163 

cor.test(taia$UT, taia$n_dighelp, method = "sp")

    Spearman's rank correlation rho

data:  taia$UT and taia$n_dighelp
S = 5620719, p-value = 0.02917
alternative hypothesis: true rho is not equal to 0
sample estimates:
     rho 
0.118835 

cor.test(taia$FA, taia$n_dighelp, method = "sp")

    Spearman's rank correlation rho

data:  taia$FA and taia$n_dighelp
S = 6614475, p-value = 0.4989
alternative hypothesis: true rho is not equal to 0
sample estimates:
        rho 
-0.03695705 

cor.test(taia$DE, taia$n_dighelp, method = "sp")

    Spearman's rank correlation rho

data:  taia$DE and taia$n_dighelp
S = 5705718, p-value = 0.05298
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1055096 

cor.test(taia$UN, taia$n_dighelp, method = "sp")

    Spearman's rank correlation rho

data:  taia$UN and taia$n_dighelp
S = 5912050, p-value = 0.1803
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.0731627 

taia_l %>%
  ggplot(aes(score, e_dighelp, color = subscale)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm") +
  facet_wrap(~ subscale) +
  guides(color = FALSE) +
  scale_color_manual(values = clrs) +
  labs(x = "TAIA subscales total score",
       y = "Estimate of dealing with digital helpers experience",
       title = "Correlation TAIA subscales with expirience of dealing with digital helpers") +
  theme(plot.title = element_text(hjust = .5))

cor.test(taia$PR, taia$e_dighelp)

    Pearson's product-moment correlation

data:  taia$PR and taia$e_dighelp
t = 6.7852, df = 335, p-value = 5.27e-11
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.2500476 0.4381609
sample estimates:
      cor 
0.3475971 

cor.test(taia$CO, taia$e_dighelp)

    Pearson's product-moment correlation

data:  taia$CO and taia$e_dighelp
t = 4.0996, df = 335, p-value = 5.199e-05
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.1144032 0.3179773
sample estimates:
     cor 
0.218567 

cor.test(taia$UT, taia$e_dighelp)

    Pearson's product-moment correlation

data:  taia$UT and taia$e_dighelp
t = 5.5088, df = 335, p-value = 7.21e-08
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.1871349 0.3832429
sample estimates:
     cor 
0.288208 

cor.test(taia$FA, taia$e_dighelp)

    Pearson's product-moment correlation

data:  taia$FA and taia$e_dighelp
t = 4.1342, df = 335, p-value = 4.507e-05
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.1162249 0.3196358
sample estimates:
      cor 
0.2203243 

cor.test(taia$DE, taia$e_dighelp)

    Pearson's product-moment correlation

data:  taia$DE and taia$e_dighelp
t = 5.7293, df = 335, p-value = 2.248e-08
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.1982204 0.3930214
sample estimates:
      cor 
0.2987294 

cor.test(taia$UN, taia$e_dighelp)

    Pearson's product-moment correlation

data:  taia$UN and taia$e_dighelp
t = 1.7091, df = 335, p-value = 0.08836
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.01400204  0.19784231
sample estimates:
       cor 
0.09297223 

taia_l %>% 
  ggplot(aes(score, n_socnet, color = subscale)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm") +
  facet_wrap(~ subscale) +
  guides(color = FALSE) +
  scale_color_manual(values = clrs) +
  labs(x = "TAIA subscales total score",
       y = "Number of social networks and social media",
       title = "Correlation TAIA subscales with number of social networks and social media") +
  theme(plot.title = element_text(hjust = .5))

cor.test(taia$PR, taia$n_socnet, method = "sp")

    Spearman's rank correlation rho

data:  taia$PR and taia$n_socnet
S = 12147347, p-value = 0.01685
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1145436 

cor.test(taia$CO, taia$n_socnet, method = "sp")

    Spearman's rank correlation rho

data:  taia$CO and taia$n_socnet
S = 14058484, p-value = 0.6065
alternative hypothesis: true rho is not equal to 0
sample estimates:
        rho 
-0.02476493 

cor.test(taia$UT, taia$n_socnet, method = "sp")

    Spearman's rank correlation rho

data:  taia$UT and taia$n_socnet
S = 11573855, p-value = 0.001069
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1563471 

cor.test(taia$FA, taia$n_socnet, method = "sp")

    Spearman's rank correlation rho

data:  taia$FA and taia$n_socnet
S = 12379302, p-value = 0.04181
alternative hypothesis: true rho is not equal to 0
sample estimates:
       rho 
0.09763564 

cor.test(taia$DE, taia$n_socnet, method = "sp")

    Spearman's rank correlation rho

data:  taia$DE and taia$n_socnet
S = 11425218, p-value = 0.0004627
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1671817 

cor.test(taia$UN, taia$n_socnet, method = "sp")

    Spearman's rank correlation rho

data:  taia$UN and taia$n_socnet
S = 12007801, p-value = 0.009219
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1247154 

taia_l %>% 
  ggplot(aes(score, f_socnet, color = subscale)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm") +
  facet_wrap(~ subscale) +
  guides(color = FALSE) +
  scale_color_manual(values = clrs) +
  labs(x = "TAIA subscales total score",
       y = "Frequency of social networks and social media use",
       title = "Correlation TAIA subscales with frequency of social networks and social media use") +
  theme(plot.title = element_text(hjust = .5))

cor.test(taia$PR, taia$f_socnet)

    Pearson's product-moment correlation

data:  taia$PR and taia$f_socnet
t = 1.4848, df = 433, p-value = 0.1383
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.02299864  0.16409771
sample estimates:
       cor 
0.07117555 

cor.test(taia$CO, taia$f_socnet)

    Pearson's product-moment correlation

data:  taia$CO and taia$f_socnet
t = 0.83383, df = 433, p-value = 0.4048
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.05418487  0.13355691
sample estimates:
      cor 
0.0400394 

cor.test(taia$UT, taia$f_socnet)

    Pearson's product-moment correlation

data:  taia$UT and taia$f_socnet
t = -0.18344, df = 433, p-value = 0.8545
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.10275052  0.08527558
sample estimates:
         cor 
-0.008815392 

cor.test(taia$FA, taia$f_socnet)

    Pearson's product-moment correlation

data:  taia$FA and taia$f_socnet
t = 0.30431, df = 433, p-value = 0.761
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.07950679  0.10849394
sample estimates:
       cor 
0.01462281 

cor.test(taia$DE, taia$f_socnet)

    Pearson's product-moment correlation

data:  taia$DE and taia$f_socnet
t = 0.51348, df = 433, p-value = 0.6079
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.06951288  0.11841428
sample estimates:
       cor 
0.02466864 

cor.test(taia$UN, taia$f_socnet)

    Pearson's product-moment correlation

data:  taia$UN and taia$f_socnet
t = -0.29625, df = 433, p-value = 0.7672
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.10811106  0.07989175
sample estimates:
        cor 
-0.01423547 

taia_l %>% 
  ggplot(aes(score, e_socnet, color = subscale)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm") +
  facet_wrap(~ subscale) +
  guides(color = FALSE) +
  scale_color_manual(values = clrs) +
  labs(x = "TAIA subscales total score",
       y = "Estimate of dealing with recommender systems experience",
       title = "Correlation TAIA subscales with experience of dealing with recommender systems") +
  theme(plot.title = element_text(hjust = .5))

cor.test(taia$PR, taia$e_socnet)

    Pearson's product-moment correlation

data:  taia$PR and taia$e_socnet
t = 4.6683, df = 433, p-value = 4.056e-06
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.1275089 0.3066146
sample estimates:
      cor 
0.2189049 

cor.test(taia$CO, taia$e_socnet)

    Pearson's product-moment correlation

data:  taia$CO and taia$e_socnet
t = 5.3414, df = 433, p-value = 1.493e-07
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.1583093 0.3348224
sample estimates:
      cor 
0.2486289 

cor.test(taia$UT, taia$e_socnet)

    Pearson's product-moment correlation

data:  taia$UT and taia$e_socnet
t = 4.0939, df = 433, p-value = 5.061e-05
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.1008503 0.2819433
sample estimates:
      cor 
0.1930402 

cor.test(taia$FA, taia$e_socnet)

    Pearson's product-moment correlation

data:  taia$FA and taia$e_socnet
t = 2.5727, df = 433, p-value = 0.01042
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.02901732 0.21425142
sample estimates:
      cor 
0.1227028 

cor.test(taia$DE, taia$e_socnet)

    Pearson's product-moment correlation

data:  taia$DE and taia$e_socnet
t = 5.7293, df = 433, p-value = 1.89e-08
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.1758227 0.3507217
sample estimates:
      cor 
0.2654548 

cor.test(taia$UN, taia$e_socnet)

    Pearson's product-moment correlation

data:  taia$UN and taia$e_socnet
t = 1.7866, df = 433, p-value = 0.0747
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.008545219  0.178131408
sample estimates:
      cor 
0.0855438 

Self driving cars and education AI

taia %>% 
  mutate_at(vars(selfdrexp, selfdrsafe, eduaiexp),
            function(x) ifelse(x < 0, NA, x)) -> taia

taia %>% 
  pivot_longer(cols = c("PR", "CO", "UT", "FA", "DE", "UN"),
               names_to = "subscale",
               values_to = "score") %>% 
  mutate(subscale = factor(subscale, levels = c("PR", "CO", "UT", "FA", "DE", "UN"))) %>% 
  ggplot(aes(score, selfdrexp, color = subscale)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm") +
  facet_wrap(~ subscale) +
  guides(color = FALSE) +
  scale_color_manual(values = clrs) +
  labs(x = "TAIA subscales total score",
       y = "Estimate of selfdriving car experience",
       title = "Correlation TAIA subscales with selfdriving car experience") +
  theme(plot.title = element_text(hjust = .5))

cor.test(taia$PR, taia$selfdrexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$PR and taia$selfdrexp
S = 265.3, p-value = 0.3702
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.2711565 

cor.test(taia$CO, taia$selfdrexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$CO and taia$selfdrexp
S = 418.25, p-value = 0.627
alternative hypothesis: true rho is not equal to 0
sample estimates:
       rho 
-0.1490473 

cor.test(taia$UT, taia$selfdrexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$UT and taia$selfdrexp
S = 175.48, p-value = 0.06984
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.5179022 

cor.test(taia$FA, taia$selfdrexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$FA and taia$selfdrexp
S = 272.56, p-value = 0.4077
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.2512199 

cor.test(taia$DE, taia$selfdrexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$DE and taia$selfdrexp
S = 326.24, p-value = 0.7359
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1037321 

cor.test(taia$UN, taia$selfdrexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$UN and taia$selfdrexp
S = 358.61, p-value = 0.9617
alternative hypothesis: true rho is not equal to 0
sample estimates:
       rho 
0.01481886 

taia %>% 
  pivot_longer(cols = c("PR", "CO", "UT", "FA", "DE", "UN"),
               names_to = "subscale",
               values_to = "score") %>% 
  mutate(subscale = factor(subscale, levels = c("PR", "CO", "UT", "FA", "DE", "UN"))) %>% 
  ggplot(aes(score, selfdrsafe, color = subscale)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm") +
  facet_wrap(~ subscale) +
  guides(color = FALSE) +
  scale_color_manual(values = clrs) +
  labs(x = "TAIA subscales total score",
       y = "Estimate of selfdriving car safe",
       title = "Correlation TAIA subscales with selfdriving car safe") +
  theme(plot.title = element_text(hjust = .5))

cor.test(taia$PR, taia$selfdrsafe, method = "sp")

    Spearman's rank correlation rho

data:  taia$PR and taia$selfdrsafe
S = 372.22, p-value = 0.9417
alternative hypothesis: true rho is not equal to 0
sample estimates:
        rho 
-0.02257133 

cor.test(taia$CO, taia$selfdrsafe, method = "sp")

    Spearman's rank correlation rho

data:  taia$CO and taia$selfdrsafe
S = 323.96, p-value = 0.7205
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1099992 

cor.test(taia$UT, taia$selfdrsafe, method = "sp")

    Spearman's rank correlation rho

data:  taia$UT and taia$selfdrsafe
S = 301.67, p-value = 0.576
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1712239 

cor.test(taia$FA, taia$selfdrsafe, method = "sp")

    Spearman's rank correlation rho

data:  taia$FA and taia$selfdrsafe
S = 217.35, p-value = 0.1723
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.4028841 

cor.test(taia$DE, taia$selfdrsafe, method = "sp")

    Spearman's rank correlation rho

data:  taia$DE and taia$selfdrsafe
S = 352.98, p-value = 0.9218
alternative hypothesis: true rho is not equal to 0
sample estimates:
       rho 
0.03026276 

cor.test(taia$UN, taia$selfdrsafe, method = "sp")

    Spearman's rank correlation rho

data:  taia$UN and taia$selfdrsafe
S = 450.47, p-value = 0.4345
alternative hypothesis: true rho is not equal to 0
sample estimates:
       rho 
-0.2375627 

taia %>% 
  pivot_longer(cols = c("PR", "CO", "UT", "FA", "DE", "UN"),
               names_to = "subscale",
               values_to = "score") %>% 
  mutate(subscale = factor(subscale, levels = c("PR", "CO", "UT", "FA", "DE", "UN"))) %>% 
  ggplot(aes(score, eduaiexp, color = subscale)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm") +
  facet_wrap(~ subscale) +
  guides(color = FALSE) +
  scale_color_manual(values = clrs) +
  labs(x = "TAIA subscales total score",
       y = "Estimate of dealing with education AI experience",
       title = "Correlation TAIA subscales with experience of dealing with education AI") +
  theme(plot.title = element_text(hjust = .5))

cor.test(taia$PR, taia$eduaiexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$PR and taia$eduaiexp
S = 136920, p-value = 5.31e-06
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.4152137 

cor.test(taia$CO, taia$eduaiexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$CO and taia$eduaiexp
S = 145289, p-value = 3.687e-05
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.3794657 

cor.test(taia$UT, taia$eduaiexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$UT and taia$eduaiexp
S = 142744, p-value = 2.094e-05
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.3903391 

cor.test(taia$FA, taia$eduaiexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$FA and taia$eduaiexp
S = 168570, p-value = 0.002786
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.2800356 

cor.test(taia$DE, taia$eduaiexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$DE and taia$eduaiexp
S = 112949, p-value = 5.1e-09
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.5175924 

cor.test(taia$UN, taia$eduaiexp, method = "sp")

    Spearman's rank correlation rho

data:  taia$UN and taia$eduaiexp
S = 159518, p-value = 0.0006156
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.3186946